# max or min

1. ### show that, at a local max/min of ||r(t)||, r'(t) is perpendicular to r(t)

show that, at a local max or min of ||r(t)||, r'(t) is perpendicular to r(t) if they are perpendicular, then \vec{r}(t) \cdot \vec{r}\,\,'(t) = 0 is this related to the gradient being a normal to a surface/curve?
2. ### absolute max/min question for function involving e

f(x) = 3xe-8x, 0 ≤ x ≤ 2 I don't know how to find the absolute maximum and minimum values. Could you show an example of how to do so, step-by-step, for this question (or a similar one)?
3. ### Critical points/ Abs. max/min values

Hey guys so I need help on two questions that I'm sort of stuck on. 1. Find the critical numbers of the given function: f(x) = 2x3+x2+2x So I got f'(x) = 6x2+2x+2 Factored out the 2(3x2+x+1) I can't factor this out anymore, so is the answer there are no critical numbers? 2. Find the...
4. ### max/min values

working on some review problems, Does anyone know how to do this question, Thanks! I know how to find the critical points with fx, fy=0 what would I do with the xyz.
5. ### max/min

A rectangular tank with a bottom and sided but but no top is to have volume 500 cubic feet. Determine thedimensions (length, width, height) with the smallest possible surface area.
6. ### max/min

there is one critical point for z=yx^5 + xy^5 + xy. Find it. Is the critical point (0,0)?
7. ### max/min

Detrmine the maximum value and the min value of f(x,y)= x^2+y^2-x-y on the closed unit disc D: x^2+y^2<=1.
8. ### Clarifying on how to make a Sign Chart for Concavity + Max/Min

Hi, I was just making sure if I was getting the hang of making a sign chart. So it's basically critical numbers of the derivative, then you would take this derivative and put it into an x and f(x) sign chart. After that you would plug in points between critical numbers to find where it ends up...
9. ### Find max/min values.

Find the max and min values of f(x,y)=x^2 + y^2 + 4 over the region R={(x,y) : x^2 + 2(y^2) =< 3
10. ### Find the extremal to the functional and discuss whether they provide a max/min

I am having a hard time getting my head around Functionals and Calculus of Variations, My question is: Given a functional and using the Euler-Lagrange equation to find an extremal, how do we show that the extremal provides a min/max (if it does) The question I am working on is J(y) =...
11. ### Help with Max/Min Problem

Here is the problem I need help with. I don't understand how to do it at all. The strength of a rectangular beam is directly proportional to the product of its width and the square of its height. Find the dimensions of the strongest beam cut from a cylindrical log of a radius 14 inches.
12. ### Calculus Question: Relative Max/Min and Inflection Points?

For the function y = f(x), the solutions to the equation 0 = f'(x) are x = -3,0,2 and the solutions to the equation 0 - f"(x) are x= -1, 2. Furthermore, f"(-2) = 7, f"(1) = -9, and f"(3) = 4. a. Where does y = f(x) have a relative maximum and where does y = f(x) have a relative minimum? b...
13. ### Multivariable calculus problem (Global Max/Min)

Find the global maximum and minimum of f(x,y) = (x^2) -2xy + 2y on the domain x ≥ 0, y ≥ 0 and y ≤ 2-x Thanks.
14. ### Max/Min problem with function unknown.

I have no idea where to start on this one. Find the side length of the largest cube which can fit inside a sphere of diameter 24cm.
15. ### Max/Min Problem...Having trouble with it?

I have absolutely no idea how to approach this question... Draw a diagram showing the region enclosed between the parabola y^2=4ax and its latus rectum x=a The, find the dimensions of the rectangle of max area that can be inscribed in this region. I drew the diagram...but so far all i have...
16. ### Max/Min Problem

Okay, so on my homework I came across the function f(x)= 10x^2*e^-x I must: a)Find the critical values b)Find the local max/min When I derived and factored, my answer was 10xe^-x(2-x) So my crit values are 0 and 2, now here is where I was tripped up: when I plugged the critical...
17. ### Extremely Hard Max/Min Problem

5. A chord joins any two points A and B on the parabola whose equation is y^2 = 4x. If C is the midpoint of AB, and CD is drawn parallel to the x-axis to meet the parabola at D, prove that the tangent at D is parallel to chord AB. I've attempted to graph the situation (attempted graph is...
18. ### Max/Min problem

determine max/min for: f(x,y)=x^2+y^2-2x-4y+2 x^2+y^2\leq 16 okey so i started with partial derivative; \frac{d}{dx}f(x,y)=2x-2\\=0 \frac{d}{dy}f(x,y)=2y-4=0 x=1 y=2 f(1,2)=-3 after that i looked at the line: x=4cost y=4sint g(t)=f(4cos(t),4sin(t))=18-8cost-16sint...
19. ### Max/Min using Lagrange

Can anyone help with this problem please? I understand the concept of the langrange multiplier but this ones stumping me. F(x,y)=2x+y subject to the ellipse g(x,y)=X^2+25y^2=1 I have f(x,y)=2i-1j. g(x,y)=2xi+50yj When I apply the lamb though I get 2=lambda 2x. Which means lambda=1/x...
20. ### Find the max/min values of s^2+t^2 on a curve by the method of Lagrange Multipliers

I've gotten an answer for the first half of this, but not the second one, which I believe is some sort of trick question. Find the maximum and minimum values of s^2+t^2 on the curve s^2+2t^2-2t=4 by the method of Lagrange Multipliers. I already have this half answered, and got the...