# points

1. ### Critical Points

f(x) = |2x|-|x - 2| Are, x = 0 and x = 2, considered as Critical Points? --------------- Our doctor said that they are not, but I argued with him that they are Critical Points. --------------- Is his statement correct?
2. ### Average distance between points on a 2-D surface?

Hi, I'm trying to work out what is the average distance between points (i.e. between grid squares) on a two-dimensional grid. Is there some formula for this? I've been told that the formula for this same problem in 3-D is... D = CUBE ROOT(Vol / N) Where... D = Average Distance between...
3. ### Find circle with 3 points

(2,1), (6,5), (0,-5) After several pages of calculations, I got nothing. I made an equation for each point, and since they were each equal to r^2, I set them equal to each other and solved for h in terms of k. You can do this three unique ways, and I got three unique values for h in terms...
4. ### critical points

Hi; Do all critical points ie local max/local min have a slope of zero. Thanks.
5. ### Lotka - Volterra problem - Critical Points of the system.

Hi, I'm trying to solve the following Lotka - Volterra model for its critical points but I am encountering some difficulty. This is the problem. I know I have to set both equations to 0, I can do this for the first one and I get x=0 and y-1 = 0, but from here I am lost. Do I sub these...
6. ### Critical points of a function

Q: For the function f(x,y)={ x }^{ 4 }+6{ x }^{ 2 }{ y }^{ 2 }+{ y }^{ 4 }+2{ y }^{ 2 }-2{ x }^{ 2 }, find the critical points and identify the character of each point. Working: partial derivatives will be: \frac { \partial }{ \partial x } =4{ x }^{ 3 }+12x{ y }^{ 2 }-4x \frac { \partial }{...
7. ### Critical points of a function

Q: Find the critical points of the function f(x,y)={ x }^{ 4 }+{ y }^{ 4 }-4xy+1 and identify the character of each point My progress so far: I have obtained \frac { dy }{ dx } =4({ x }^{ 3 }-y) My understanding is that to find the critical points, dy/dx should be equated to 0 and solved as...
8. ### find the angle between two lines formed by three points in n-space

Hello, I wasn't sure where to post this, so please feel free to move it. In some ways, I suspect this is a very elementary question for an expert, so I posted in on the pre-university side. Here is an example in 2D of the problem I am looking at, given three sets of coordinates...
9. ### Calculating maximum and minimum points of a cubic WITHOUT calculus

Hi everyone I wanted to ask a question about calculating maximum and minimum points. I understand it is the easiest way of calculating maximum and minimum points using differentiation. But what I wanted to ask was is it possible to calculate the maximum and minimum points of a cubic function...
10. ### critical points of a function

Hey I have the following funcion and I need to find its critical points. f(x)=x/(x^2-4) If derivative is equal to zero: f'(x)=-x^2-4/(x^2-4)^2 0=-x^2-4 x^2=-4 Absurd! Therefore, don't exist a point "c" such that f'(c)=0 My question is: Can I consider that x=2 and x=-2 are critical points...
11. ### Points on a circle

I need help solving this one. Dont even know where to start. Thanks, Jackson
12. ### Points horizontal to tangent plane - Clac 4

Given the surface X2+Y2/9+Z2/9=1 Find the equation of the tangent plane with the points (1/3,2,2) In doing this I found the tangent plane to be Z=-1.5x-y+4.5 The question then asks for you to find a point at which the tangent plane to this surface is horizontal and if there are any such points...
13. ### Finding critical points and others from an equation

g(x) = -3x^3 + 2x^2 + x - 7 Use calculus to answer the following questions. Express your answer exactly, do not round. a. Find all critical points (x-values) and label them as a local max, min, or neither. b. Find all inflection points c. On what interval is g(x) increasing d. On what...
14. ### Perspective geometry - vanishing points problem

Hi everyone, I'm a beginner self-taught artist and I have a following geometry (2 point perspective) problem. (see picture) Lines a and b meet at VP2 and lines c and d meet at VP1 vanishing points. I need to find the yellow line that goes to the VP1 in the "middle" between c and d. By drawing...
15. ### Probably really simple question about math, and ICEEs.

Hello everyone! This is my first question here. I hope I have used the correct forum group. This is probably really simple, but I just can't get my mind around it. I want to redeem "ICEE points" for ICEE stuff (ICEE stuff is the offical name for the products). I can pay for each item I am...
16. ### Enumerating two circles intersect transversally at two points in a standard torus

Hi; Let T be a standard torus in R^3. Let C_1 and C_2 be two circles in T such that C_1 and C_2 intersect transversally at two distinct points, say p and q. By transverse intersection I mean tangent intersection is not allowed. Orient C_1 and C_2 and let l_1 be an arc in C_1 from p to q...
17. ### New thought experiment with infinity - circles with infinite points inside them

(sorry, I don't know in which section I should post this question) I now think I have some idea why Cantor (or whoever it is) said things like "there are more real numbers R than whole numbers N." So I think I've understood the concept of comparing infinite sets. And why this is...
18. ### 4 points in a plane 3D

I want to know how to find that given 4 points that they are in a plane (3D) There are 4 points with coordinates (3D) x1,y1,z1 =0,0,1 x2,y2,z2 = 0,1,2 x3,y3,z3 = 0,1,3 x,y,z = 1,0,0 One can see that the 4 points are not in a plane but I want to know the formulas to see for other points...
19. ### Intersection points between circle and parabola

Hello, I'm trying to find how many points a certain circle and parabola intersect (see attachment). Equation for circle is x^(2) + y^(2) =9 and for the parabola y=(x+3)^(2) -2. The answer is 2. Without a graphing calculator, what is a simple way to solve this? I set the equations equal to one...
20. ### Showing there is a dense set of singular points when |z| = 1 for a power series

I've been stuck on a complex analysis problem with showing there is a dense set of singular points for the power series \sum_{n=0}^{\infty} z^{2^n} I'm guessing I should use the rationals, but I really don't know where to go beyond there. I can parametrize the unit circle with e^{2\pi i\theta}...