# Tagged Questions

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### Is the following graph having two local minima

https://www.desmos.com/calculator/abuvb1zdkb I think yes, the main question i think is of the definition of neighbourhood For a function with domain $(-\infty, -3)\cup (3, \infty)$  Is -3 in ...
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### For which real numbers $c$ is there a straight line that intersects the curve $y = x^4 + 9x^3 + c x^2 + 9x + 4$ in four distinct points?

For which real numbers $c$ is there a straight line that intersects the curve $y = x^4 + 9x^3 + c x^2 + 9x + 4$ in four distinct points? I don't quite the understand the solution which is in ...
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### Find the slant asymptote for $x= \dfrac{3t}{1+t^3}$, $y= \dfrac{3t^2}{1+t^3}$

I am geting $y=-x$, while the answer $y=-x-1$ What i did is to write $y = tx$ and as $t$ goes to $-1$. $x, y$ go to $\infty$, hence the asymptote is $y=-x$ Where did i go wrong.
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### What is a French curve, as mentioned by Feynman?

I'm reading "Surely You're Joking, Mr. Feynman!", he says: I often liked to play tricks on people when I was at MIT. One time, in mechanical drawing class, some joker picked up a French curve (a ...
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### What is the graph of $y = \sin n$ and why is it different from the graph of $y = \sin x$?

I have downloaded a book about Calculus from MIT OCW. In that book, there is a section "A Thousand points of Light". (You can download the relevant section from here.) In that section, it is written ...
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### Rewrite the following surface so that I can graph it.

$z = \dfrac{1+x^2}{1+y^2}$  I want the part of the surface above the square $|x|+|y|\leq 1$  OR we can write this square as $-y<x<y$ and $-1<x<-1$  I have spent hours trying ...
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### Establish the absolute maximum of a function

We have this function:$$f(x)=\begin{cases} \sin(x) \cdot\ln(\sin2x), & \mbox{if }0<x<\pi/2 \\ 0, & \mbox{if }x=0,\mbox{or }x=\pi/2 \end{cases}$$ So, how to prove that it decreases and ...
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### By looking at a graph of a function, how do I find the maxima/minima of its curvature function. [closed]

All Ideas are appreciated. I could think of some intuitive ideas, but could not back them by solid clean reasoning. thanks, I will post If i find anything
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### Increasing, continuous, concave downward function normalised between 0.5 and 1

What would be a good function which is increasing, continuous, concave downward with $$\lim_{x \to 0} f(x) = 0.5$$ and $$\lim_{x \to \infty} f(x) = 1.$$ It should be concave downward whose ...
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### Plotting the intersection of multiple surfaces with WolframAlpha

I want to plot the intersection of two surfaces like in this post. But if I enter the much simplified expression ContourPlot3D[{x^2 + y^2 + z^2 - 4=0, xy=1}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}] ...
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### How to draw the graphs for these functions?

Could I please be helped with the graphs for the following functions: $$y=\lceil \tan x \rceil, \quad y=\tan (\lceil x \rceil), \quad y=\lceil \tan (\lceil x \rceil) \rceil$$ I have been able to ...
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### Mathematical/graphical implications of representing double integral of changing acceleration (which gives displacement) on a 3d plane.

Lets assume a function a = |sin t| for acceleration over time. If we integrate it, we get instantaneous velocity. I have been told that integrating a function provides me with the area under the ...
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### Integrating function of acceleration to obtain displacement

Lets assume a function a = |sin t| for acceleration over time. If we integrate it, we get instantaneous velocity. Now i have taken a limit for time. How will this graph look like? I have been told ...
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### Finding the area of a region?

I sketched out the graph to get this figure but I can't seem to find the area of the shaded region... would one Y = 4 and the other Y = 8? I, in all honesty, am so flabbergasted with this question, ...