# extreme

1. ### Justifying an extreme value theorem?

I was looking through the coursework document on college board and one sentence says there are three ways to justify an extreme value. What are these three ways?
2. ### local extreme value

2(x^3) +(y^3) +3(x^2)- 3y - 12x -4=0 Find the local extremum of function i followed the steps to find the critical point first . But , i got fx = 6(x^2) + 6x -12 = 0 , x = 1 , -2 fy = 3(y^2) -3 = 0 , y = 1 , -1 I only found these...How to form the critical points ?
3. ### Finding local extreme of a function with fractional powers

Where did the 3 come from (highlighted in yellow)? Click the image to see the problem and work.
4. ### extreme values

Hello! How can I find out the min and max for sin 3x + sin 5x? thank you! :)
5. ### Extreme values

Just double checking to make sure I got the correct answer because it is not the answer the book gives. I need to find the maximum and minimum value \frac{4x}{x^2+1}, -2<x<4 so I got the derivative and solved for f'(x) = 0 the derivative being \frac{4x^2-8x+4}{(x^2+1)^2} \Rightarrow x = 1...
6. ### Is this function consistent with the Extreme Value Theorem?

PROBLEM: What are the maximum and minimum values of the function y=|x| on the interval -1{\leq}x<1? Notice that the interval is not closed. Is this consistent with the Extreme Value Theorem for continuous functions? Why? ATTEMPT: I think I have the right answer, but I want to make sure it is...
7. ### Explanation of the Extreme Value Theorem proof

In the proof to this theorem, how does taking the supremum of (8), yield the contradicting inequality? We know from the premises that f(x) < M, for all x in I. However, the statement f(x) <= M - (1/C) for all x in I does not in any way lead to the contradiction stated in the proof. Here is my...
8. ### Calculate asymptotes and local extreme values

I'm fed up with this question from my book. I've calculated the constants to this equation but got stuck at the asymptotes and local extreme values calculations which I need to plot the graph, perhaps anyone could help me out or guide me towards the solution of calculating the asymptotes/local...
9. ### Determining absolute extreme of function

f(x)=x2+2x-4 Interval is [-1, 1] What I did: f'(x)=2x+2 x=-1 Plugged in: One of my minimums is (-1, 0) I'm confused on how to get the maximum now. I did 0=x2+2x-4 4=x(x+2) 4/(x+2)=x But I don't think this is correct. Please explain. Thanks!
10. ### evaluatng others from extreme value of one function

Suppose f is differentiable on -infinity and +infinity(everywhere) and assume that it has a local extreme value at the point (2,0). Let g(x)=xf(x)+1 and h(x)=xf(x)+x+1 for all values of x. Evaluate g(2), h(2), g'(2) and h'(2).
11. ### Another local extreme problem

I am facing another problem that I can't compute the extremes for:(Doh) f(xy)=ex(x2-y2) so far I have: fx= 2xex + ex(x2-y2) fy= -2yex fxx=2ex+2xex + ex(x2-y2) + 2xex fyy= -2ex fxy= -2yex How do I find the extremes? I set fx and fy to 0, but I can't solve for x and y. Thanks for any help.
12. ### find the extreme points

[SOLVED] find the extreme points Find all extreme points to f\left( x,y \right)=\left( x^{2}+y^{2} \right)\left( xy+1 \right) --- Not to important, but I'll put it here anyways. The original question is this "Problem: 3c) Are there any other extreme points than those in 3a)? See image...
13. ### find Extreme values of f(x,y) , subject to g(x,y)

Extreme values of f(x,y) = (x-1)^2 + (y+2)^2 on the circle x^2 + y^2 = 5 I thought it was done by fx = λgx => 2(x-1) = (2x)λ and fy= λgy => 2(y+2) = (2y)λ but λ is meant to be a constant.
14. ### Finding extreme point in a multivariable function

Hello, As far as I know, critical points are the point in which the gradient equals zero or not defined. In the following functionZ=X(1+Y)^{1/2}+Y(1+X)^{1/2}, the gradient is not defined for all X\leq-1 or Y\leq-1. How do I prove that only (-1,-1) is an extreme point (maximum)? Thanks in...
15. ### Advanced Geometry - Convex sets and Extreme points proof

Let K subset of R^n be a convex set. We call x1 element of K an extreme point of K if K/{x1} is convex too. Prove that x1 element of K is an extreme point iff cx + (1-c)y = x1 for 0<c<1, c element of R (real numbers as above) implies x = y = x1. any answer or help will be greatly...
16. ### Distribution of the extreme value of a non-stationary Gaussian process

Let P be is a non-stationary Gaussian process. I would like to know the CDF of its extreme value (e.g. its maximal) over a period of time [0,t]. I know that no analytical ways for doing so. Is there any approximation to the CDF?
17. ### intermediate and extreme value theorms?

I need help with starting the question below. I believe I have to use either intermediate-value or extreme-value theorems, however, I am not sure. The question is as follows: Fix positive number P. Let R denote the set of all rectangles with perimeter P. Prove that there is a member of R that...
18. ### unique value and extreme point question

4)a) prove that g(x)=e^{x}+\frac{x^{3}}{x^{2}+1} gets a unique value for every x in R 4)b)prove that f(x)=e^{x}+\frac{x^{2}}{2}-\frac{ln(x^{2}+1)}{2} gets total minimum (not only local) you can use part 4a) 4)c)prove that \frac{ln(x+1)}{x} 'uniformly' continuous in (0,\infty)
19. ### differentiability and extreme points question

2.b) f is continues in [0,1] and differentiable in (0,1) f(0)=0 and for x\in(0,1) |f'(x)|<=|f(x)| and 0<a<1 prove: (i)the set {|f(x)| : 0<=x<=a} has maximum (ii)for every x\in(0,a] this innequality holds \frac{f(x)}{x}\leq max{|f(x)|:0<=x<=a} (iii)f(x)=0 for x\in[0,a] (iii)f(x)=0 for x\in[0,1]...
20. ### Question regarding these two extreme values problems...

So I'm on the last two problems of this assignment and I've worked them both out as far as I can and I can't seem to figure out where I'm going wrong. Both of them have to do with extreme values and the 1st and 2nd Derivative Tests. Here's the first: f(x) = \cos (x) + \frac{\sqrt{2}}{2} x...