Questions tagged [slope]

For questions on finding or applying slope, a number that describes both the direction and the steepness of a line.

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Intuitive Way to Find Maximum Gradient of a Bezier Curve

I'm trying to find if any point on a bezier curve has a slope that is lesser than some predetermined angle, let's say $45^\text{o}$. For certain cases I can see that the answer is obvious. Like ...
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1 vote
2 answers
52 views

How to bring $\log(y) = \log(a) + \log(e^{bx})$ to $y=mx+c$ format?

I was solving a problem regarding equation of the straight line. The question is to find the best value of $a$ and $b$ if $$ y = ae^{bx}. $$ What I tried? I multiplied LHS and RHS with $\log$ in order ...
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0 votes
1 answer
32 views

How to reshape a nonlinear curve into a linear curve?

I have this data: ...
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3 votes
3 answers
84 views

A Pseudo-Derivative for $f(x)=|x|$

I was wondering what the significance of a function that gives the slope of $y=|x|$ at any $x$ is. If$$f(x)=|x|$$then we could do, as the derivative:$$\frac{d f}{d x}=\frac{x}{|x|}$$or$$\frac{d f}{d x}...
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0 votes
1 answer
29 views

What is the 'slope' of a function that has x, instead of y as the subject, called?

We are all familiar with y = mx + b, the slope-intercept form with y as the subject: m is the gradient - how much y changes by an increase in x of 1. b is the y-intercept - the value of y at x = 0. ...
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3 votes
1 answer
70 views

A Transylvanian Hungarian MC Problem.

question Show that there exist infinitely many non similar triangles such that the side-lengths are positive integers and the areas of squares constructed on their sides are in arithmetic progression. ...
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3 votes
3 answers
195 views

Differentiability of a piecewise defined discontinuous function

Let $ f(x) = \begin{cases} x-4 & \text{if } x \lt 1; \\ x+1 & \text{if } x > 1; \\ 0 & \text{if } x = 1. \end{cases}$ Why isn’t this function differentiable at 1? Why isn’t its ...
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-1 votes
2 answers
130 views

Why is $\frac {d}{dx} (x^2) = 2x$ not $x$?

I am new at calculus and so I am studying derivatives now. We know that, $$\frac {d}{dx} (x^2) = 2x$$ I know the proof of it by the first rule derivatives. But still, my question is why. It is simply ...
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0 votes
1 answer
24 views

Rigorous proof of intersection of straight line and two graphs in a translation relationship

The question is : $f(x) = \log_3 x, g(x) = \log_3{(x+3)+4}$ There are two intersections $\mathrm A$ and $\mathrm B$ made by $y=-{4\over 3}x+4$ $\overline {\mathrm {AB}} = ?$ It was obvious by the ...
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Slope of Tangent line of Polar Curve at Point

Question We had an examination today in college and the question was this: Find the slope of the tangent line of polar curve $r = 3(1-\cos\theta)$ at point $B(\pi/3, 3/2 )$. Answers are: $2\pi$, $\pi/...
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2 votes
0 answers
50 views

Doubt regarding finding the gradient of of a scalar field

I am new to vector calculus. I watched few you tube videos and came to the conclusion that directional derivative is something like slope with direction and its ...
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0 votes
2 answers
60 views

Find the Point/s on the Curve $y-x^3=0$ where the normal line have a slope of $\frac{-1}{3}$.

I am bit clueless on how to start the problem. The only idea I have is to use derivatives, yet I can't continue on. I have tried researching different problems connected to it as well, but the results ...
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0 votes
0 answers
13 views

negative slope of a triangle given only the sides

So my teacher gave me this graph and I needed to calculate the slope of the hypothenuse or f'(0.25). So 62/121 is positive and I can see that the slope is negative....
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2 answers
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How to prove this hypothesis regarding slopes and ellipses?

Let $a, b\in \mathbf{R}^+, \lambda >1$. $\Omega: \dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$, Point $M(\dfrac a{\lambda}, 0), A(-a,0),B(a, 0)$. Let line $l$ pass through $M$ and intersect with $\Omega$ at ...
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3 votes
2 answers
66 views

A question regarding the point-slope formula : does the formula really hold for any point of the straight line?

I can see only one way to derive the point slope formula, but this derivation also seems to bring a question. Let $D$ be the straight line of slope $m$ passing through point $P=(a,b)$. Let $Q=(x,y)$ ...
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1 vote
0 answers
56 views

"Slope" in mathematics and " slope" in economics.

Note : I mainly consider the case in which demand curves are linear , to keep things simple. I'm having trouble in applying mathematics to (micro)economics due to the fact that in this discipline , ...
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1 vote
2 answers
37 views

Find the equation of a line that is tangent to both parabolas simultaneously [closed]

Consider the parabolas $y=x^2$ and $y=x^2-2x+2$. How to find the equation of a line that is tangent to both of them at the same time? Please, walk me through the most intuitive solution.
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1 vote
1 answer
33 views

How the slope of increase of length of shadow can be obtained from speed of walking?

The critical part which I want to discuss is painted with red below. A light on top of a lamppost shines$~25~\mathrm{ft}~$above the ground. A main$~6~\mathrm{ft}~~$tall is walking away from the light....
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2 votes
3 answers
96 views

Is there a relationship between slope of the curve $ f(x, y) = 0 $ and the partial derivative $ \frac{\partial f}{\partial x} $?

Let $ f(x, y) = 0 $ define a curve. Is there any relationship between the slope of this curve and the partial derivative $ \frac{\partial f}{\partial x} $? For example, if $ f(x, y) = (x - 1)^2 + (y - ...
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1 vote
0 answers
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How do I write a formula for a slope, based on certain values?

First, Thank you for taking the time to read this. Although I love math, my skills are nowhere close to be able to solve my problem. I am a hobby programmer, but all my education is in biology and ...
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0 votes
0 answers
22 views

Slope of multidimensional line in regression

lets say I did a regression problem and I got weights = [w0,w1,w2,...wn], with n a large number. How do we find the Slope of this line? I know how to do slopes in 2D, but I'm having difficulty ...
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0 votes
0 answers
10 views

Compute 3D accelerometer reading in presence of slope

Let $E$ be a 2D matrix representing an area, with $E[i, j]$ indicating the elevation in meters at position $i, j$. This representation has a certain resolution of $m$ meters per tile. From $E$ I can ...
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1 vote
1 answer
27 views

Creating a change in X and Y with an angle.

I am coding a small game in JavaScript and I am running into a math problem. I am trying to move an object towards the location that I just clicked. I am able to successfully do this with the code ...
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0 votes
1 answer
92 views

Slope of bézier curve, with t not between 0 and 1

I work with so called "animation curves" in Unity which are basically bézier curves. For an algorithm I need to know the slope of the curve at point t. I already found some solutions on the ...
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1 vote
0 answers
45 views

Function with equal nth derivatives to two functions at two points.

I have a function, $p(x)$, connecting two functions, $a(x)$ and $b(x)$, at two separate points. The first derivatives are also equal at those points. The following equation is a representation of $p(x)...
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0 votes
0 answers
53 views

Relation between given points in a line

Which formula can I use for getting the relationship given below, from the geometry described in the picture? How can I relate these 2 points given? $$k=R \left( \frac{\omega_c}{1-e^{-RTs/L}} \right)$$...
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0 votes
1 answer
39 views

Given the line between points 1 and 2, what is the change in angle to point 3?

I have polylines in an database table. ...
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0 votes
1 answer
26 views

Does every possible slope field represent some first order differential equation?

Just started learning about Differential Equations in Khan AP Calc class. I'm wondering if every possible slope field could be said to represent some first order differential equation. Or could you ...
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-2 votes
2 answers
23 views

How do I find point B of line AB with only point A, distance, and slope? [closed]

Good morning. There is a line AB and A is at point (x, y). x and y are known. So is the slope (m) and distance (time). Is there a formula to calculate the x and y value separately of point B?
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0 answers
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Estimating the slope of the an exponential growth

I want to estimate the slope of the following exponential growth The simplest way I see is to assume that the exponential growth can be approximated with a straight line. Then we write down a right ...
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  • 1,089
0 votes
3 answers
99 views

How to find the slope of a line given one point and the fact that it runs tangent to a circle

There's a circle with radius = 8 feet The center of the circle is the origin A person is situated at (12,0) and their line of sight runs tangent to the circle The problem is to figure out which ...
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5 votes
5 answers
839 views

Why $f(x) = x^2$ has variable derivative but its tangent has constant slope?

I'm taking Brilliant.org's calculus course, and I'm on the section called The Derivative. My (mis)understanding: A tangent line is a linear function that grazes a point, $a$, on the graph of a ...
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0 votes
1 answer
138 views

Can a linear function have zero slope?

Can we say function $$y=f(x)=10$$ is a linear function? Can a linear function have zero slope?
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0 votes
0 answers
13 views

Validity of scatter plots for multivariate regression

I was just wondering how reliable scatter plots are in the context of multivariate regression. Say, for example, I want to fit the following model: ...
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1 vote
0 answers
39 views

What is the equation of a curve with negative slope that gets gradually flatter?

I'm taking grade 12 chemistry and there is a curve per the subject line and sorry to visually impaired but I need to paste an image as I'm not good at describing but it's basically looks like half a ...
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0 votes
1 answer
40 views

How to understand function with same gradient but “reflections” of each other??

Came from a homework question but two different but same answers. two approach, but reach equivalent answers fine. Checked with differentiation, Fine However, the graphs look like reflections of ...
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0 votes
0 answers
51 views

I understand $\tan(slope) = \frac{\text{difference of elevation}}{\text{horizontal advancement}}$ but cannot figure $\tan(slope) = \sqrt{b^2 + c^2}$

I understand the calculation of a slope with the formula $$ \tan(slope) = \frac{\text{difference of elevation}}{\text{horizontal advancement}} = \frac{3}{5} = 0.6 $$ But a book about Geographic ...
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0 votes
1 answer
78 views

Why am I getting two slopes on differentiating the standard parabola equation?

$y^2=4ax$ $y= \pm 2 \sqrt {ax} $ Now, we have two cases. And after differentiating both we get two different slopes which is not possible. $\frac {dy}{dx} = \pm \frac {2a}{y}$ What am I doing wrong?
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0 votes
1 answer
36 views

Comparing a two different sequences of values to a third, correct sequence, and determining which of the two is more accurate.

I have a question in mind and would be thankful for any help: Consider some values: $a_1, a_2, \cdots, a_n$. Assume that these values are the true, correct values. Now consider two other sets of ...
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  • 101
1 vote
0 answers
64 views

Can the "Instantaneous rate of change" ever be an exact value?

I was taught in my University's Calculus 1 course that the derivative of a function at a point is its "Instantaneous rate of change" , it was defined using this limit: $lim_{h \to 0} \frac{f(...
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1 vote
1 answer
51 views

Name and/or generalization? "The slope of the secant through two points of a quadratic is the average of the slopes of the tangents at those points."

Does the following property of quadratic equations have a name? Is it generalized in some way? Or generalized to other functions? Pick any two points on the graph of any quadratic. Draw a secant ...
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1 vote
1 answer
46 views

How to find the vertices of a rectangle when the slope of the direction is given?

The title might be a bit confusing but I'll do my best to explain this. So this image is given: The coordinates of vertex A are (3,2). We also know that [AD] and [BC] measure 1 unit each and [AB] &...
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2 votes
0 answers
29 views

Finding the two suitable points among $n$ points

I have $n$ points in the $xy$-plane; $(x_1,y_1), \dots , (x_n,y_n)$. I want to find the following: the two points that form a line with greatest slope. the two points that form a line with least ...
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0 votes
0 answers
76 views

How do we know that the slope of a curve is constantly changing?

(Please don't use calculus in your answers as I'm attempting to learn differentiation through this question. You can use limits; I understand limits. Thanks!) Consider $y=x^3$: (Let us consider only ...
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0 votes
1 answer
23 views

Points on a line distant from a given point on the line

I have a line with slope given as the pair: dx, dy (slope: dy/dx). Given a point (x, y) on the line, what are the coordinates (x(d), y(d)) of the 2 points such that the distance from (x,y) measured on ...
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0 votes
1 answer
39 views

How to Compute the Point Slope?

Assume I have points $(125,1)$ and $(5000,20)$. The slope would be $m = \frac{y_2 - y_1} { x_2 - x_1}$ or $256.5789474$, right? Assume the slope and one point are known, I should be able to compute ...
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1 vote
3 answers
96 views

If $P(1,2)$, $Q(−3,2)$ and $R(3,−2)$ are the vertices of the triangle $PQR$, then find the value of $\tan Q$.

If $P(1,2)$, $Q(−3,2)$ and $R(3,−2)$ are the vertices of the triangle $PQR$, then find the value of $\tan Q$. I am unable to solve for $\tan Q$. I constructed the triangle $PQR$ and measured $\alpha$....
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1 vote
2 answers
193 views

Prove that three points lie on a semicircle

I have three points $A(-10,-12)$, $B(6,18)$, $C(-2,-14)$. I have to prove they exist on the same semicircle. How? If I try to draw the three points to investigate I see that I can draw a right ...
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4 votes
4 answers
407 views

What is the tangent to this equation at origin?

$$x(x^2 + y^2) = a(x^2 - y^2)$$ I was trying to find the equation of the tangent as $$(Y-0) = \frac{dy}{dx}(X - 0)$$ where $$\frac{dy}{dx} = \frac{2ax-3x^2-y^2}{2(x+a)y}$$ So here putting the values ...
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1 vote
2 answers
90 views

Determine the differentiable function $f$ whose graph lies above the x-axis and passes through the point $(0, 1)$

I'm trying to solve the question: Determine the differentiable function $f$ whose graph lies above the $x$-axis and passes through the point $(0, 1)$ and such that for any $x\geq0$ the area under the ...
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