4
votes
1answer
45 views

Speediness and correctness when graphing by hand .

First of all thank you for visiting this question! I believe it's a pretty simple problem but get's kinda hairy and time consuming on each step as I have done it, so my question (the one you are here ...
1
vote
1answer
65 views

Describe the graph of f if the graph of its integral its given

Describe the graph of $f$ if the graph of its integral $g(t) = \int_{0}^{t} f(s) ds $ is: graphic of g graphic of f I analyze the derivative and the sign of the derivative and try to find ...
5
votes
5answers
113 views

Points on $(x^2 + y^2)^2 = 2x^2 - 2y^2$ with slope of $1$

Let the curve in the plane defined by the equation: $(x^2 + y^2)^2 = 2x^2 - 2y^2$ How can i graph the curve in the plane and determine the points of the curve where $\frac{dy}{dx} = 1$. My work: ...
1
vote
1answer
32 views

description of the function whose graph corresponds to Figure

Consider f be a real continuous function , $f(0) = 0$ , and whose graph has the form shown in the figure: a) How can a give description of the function whose graph corresponds to Figure. b) Sketch ...
1
vote
2answers
62 views

How can the point of inflection change before the vertical asymptote?

I have to draw a graph of a function which seems to have an inflection point AFTER the vertical asymptote. i.e. f(x) = $\tan^{-1}\left({\frac{x-1}{x+1}}\right)$ Using the quotient rule, I get... ...
1
vote
1answer
32 views

Are intervals considered local min/max values of a function?

If you have a function with an interval. i.e. $y = 5x$ where $0 \leq x \leq 5$ Obviously the function itself has no local min/max, but if the function is only for the interval between $0$ and $5$, ...
0
votes
2answers
1k views

How can you find the x-coordinate of the inflection point of the graphs of f'(x) and f''(x)?

So I understand how to find the inflection points for the graph of f(x). But basically, I have been shown a graph of an example function f(x) and asked the state the inflection points of the graph. ...
1
vote
1answer
75 views

Function with a constant infinite order derivative, infinite final value, 0 initial value, and graph that resembles geometric growth

Please forgive my vocabulary & usage because I'm only a math amateur, so I'll try to describe this the best I can. Does such a function exist that has an infinite order derivative with a constant ...
3
votes
3answers
152 views

How do computers draw function graphs?

Could anyone give me a general overview of the algorithm computers use to draw graphs? I'm guessing it is either by graphing many, many points and just connecting them or by doing a general study of ...
1
vote
1answer
56 views

Study of a trigonometric function

Today I was studying this function $\displaystyle{y=\sin \left|x \right|+\left|\cos x \right|}$ and I tried to draw its graph using my knowledge so I started from the domain which is $∀x \in\mathbb ...
0
votes
2answers
112 views

Derivative & Turning Point Relationship

Can someone explain the link between the turning point (local max, min & stationary point of inflection) and it's relationship to derivatives. Let me clarify what I understand (feel free to ...
0
votes
1answer
41 views

A problem about a calculus equivalence of inflection point

The problem: Given $f: D \rightarrow \mathbb{R}$ a differentiable function on the interval $(a,b)$, and $g: D \rightarrow \mathbb{R}$ satisfying: $$g(x) = \begin{cases}\dfrac{f(x)-f(x_0)}{x-x_0} ...
0
votes
2answers
53 views

Use a graph to estimate the time at which the number was increasing most rapidly

For the period from 2000 to 2008, the percentage of households in a certain country with at least one DVD player has been modeled by the function $f(t) = \frac{87.5}{1 + 17.1e^{−0.91t}}$ where the ...
1
vote
2answers
315 views

Finding all local maximum and minimum points of function

If $$f(x) = \left\{\begin{array}{lr} x, \ \text {if x is rational}, \\ 0, \ \text {if x is irrational}, \end{array}\right. $$ Find all local maximum and minimum points of $f(x)$. How can I go about ...
0
votes
1answer
48 views

A basic question on second derivative of $f(x)$

Is there any general shape of a curve for which $f''(x) >0$ for all $x$ ? the same question for $f''(x) < 0$ for all $x$
0
votes
2answers
175 views

Determine an equation for the tangent to the graph of f(x) at point P.

Determine an equation for the tangent to the graph of f(x) at point P. Use of CAS tool allowed. a) f(x)= 3/(1+√x) , P(4, 1) ...
0
votes
1answer
119 views

Rate Of Change & First Derivative

I have some data in Seconds (X axis) and % (y axis). Lets say for ten seconds the data below: S = 0 % = 0.1 S = 1 % = 0.2 S = 2 % = 0.3 S = 3 % = 0.4 S = 4 % = 0.5 S = 5 % = 0.6 S = 6 % = 0.7 ...
2
votes
2answers
93 views

How to show that $f(x)-x \times df(x)/dx ≥ 0$ when f(x) is concave?

How do you intuitively (perhaps even graphically) show that $f(x)-x {{df(x)}\over{dx}} ≥ 0$ when the function $f(x)$ is concave, e.g. when ${{df(x)}\over{dx}}>0$ and ${{d^2f(x)}\over{dx^2}} < ...
0
votes
1answer
96 views

How can I calculate the derivative of the derivative using the tangent line?

How can I calculate the derivative of the derivative of a function $ f(x) $ using the tangent line of a point from that function $ f(x) $ ?
1
vote
1answer
63 views

Number of points of non-differentiablity in a graph

Hahaha it seems all my questions are going to be calculus-based. :P Another doubt, here's the question: Let $f(x) = \max(\cos x,\hspace{2mm} x, \hspace{2mm}x-1)$, where $x \geq 0$. Then number of ...
5
votes
4answers
159 views

How can a point of symmetry have a slope which isn't either $0$ or $±\infty$?

I've got a bit of a doubt with a question I'm solving. It goes like this: For $a>0$, let $f:[-4a,4a] \to R$ be an even function such that $f(x) = f(4a - x) \hspace{2 mm}\forall x \in [2a, ...
9
votes
1answer
321 views

Doubt regarding calculus, graph of functions, point of inflection.

We're studying the application of derivatives in mathematics right now. This refers to a question which arose in my head while solving a particular problem. The problem was: A function $f(x)$ is ...
0
votes
2answers
56 views

Graphing $y= \frac{x^3}{x^2-1}$

I'm having a lot of problems trying to graph this... other than using a graphics calculator! I know the domain is all real values of $x , x$ does not equal $-1 \text{or} 1$. The point of inflection ...
0
votes
1answer
35 views

Taking the derivative from a graph?

I have a problem that's graphed. It's linear from $(0,0)$ to $(1,1)$, then it's a horizontal line after that. I have to find four derivatives from this, and I've never done a problem like this ...
1
vote
1answer
369 views

Bezier Curves and Acceleration

So I'm working on a program that graphs a bezier curve by manipulating the control points. This curve represents the velocity of something over time; I also want the option manipulate it all in terms ...
4
votes
2answers
743 views

Slope of a nonlinear curve at a single point

This part of my microeconomics lesson plan has me baffled. Consider for example the nonlinear continuous and differentiable function Y = f(X) = X 2 + 4. Suppose we want to know its slope at the ...
-1
votes
2answers
82 views

computing derivatives using a given graph

I know $f'(1/2)= 1$ because the professor did that part of the problem in class. But unfortunately I just cannot see the logic to complete the rest of the problem. This problem is supposed to be ...
3
votes
1answer
2k views

How to derive the equation for a bézier curve

So, I remember a while back there was a maths competition and we were given a curve that we needed to write an equation for. I just skipped the question since I didn't even know where to begin. I ...