Posted by **Lucy** on Tuesday, February 28, 2012 at 12:39am.

using the chain rule find the min and max points and their values of the composite function defined by z=x^2+y^2, x=sin(2t), y=cos(t)

This is what Ive got so far...

dz/dt= 2x*dx/dt+2y*dy/dt

=4sin2tcos2t-2sintcost

I understand the steps of computing the max and min I just can't seem to solve this problem. Its on a test I have due tomorrow so please help!!

- Please help for my test CALculus -
**MathMate**, Tuesday, February 28, 2012 at 8:45am
You need to find dz/dt=0, so set

4sin2tcos2t-2sintcost =0

Expand using double-angle formulae:

8cos(t)sin(t)(cos(t)^2-sin(t)^2)-2cos(t)sin(t) = 0

Factorize:

-2cos(t)sin(t)(4sin(t)^2-4cos(t)^2+1)

Which gives

t=0, t=π/2, t=π and t=3π/2

when sin(t)=0 or cos(t)=0.

This leaves us with:

4sin(t)^2-4cos(t)^2+1=0

which can be reduced by the substitution

cos(t)^2=1-sin(t)^2

to a quadratic equation equivalent to

sin(t)=sqrt(3/8)

Now that leaves you to check each point as a maximum/minimum or inflection point using second derivatives.

- Please help for my test CALculus -
**zack**, Thursday, November 3, 2016 at 3:23pm
vai toma no cu

- Please help for my test CALculus -
**pirocudo kid bengala**, Thursday, November 3, 2016 at 3:24pm
vai te fude caralho nao fode nao vai estudar nao tem essa de ficar pedindo ajuda pr aprova na net ta xapada de nescau caraio

- Please help for my test CALculus -
**pirocudo kid bengala**, Thursday, November 3, 2016 at 3:26pm
piranha fodida

## Answer This Question

## Related Questions

- cal3 - Using the chain rule, find the min and max points and their values of the...
- calculus - find max, min and saddle points of the give function f(x,y)=sin(x)+...
- Calculus - Find f'(x) if f(x)=sin^3(4x) A. 4cos^3(4x) B. 3sin^2(4x)cos(4x) C. ...
- Calculus - I have y = sin^2(3^(x)) which I rewrite as y = (sin(3^(x)))^2 I got ...
- Calculus - Find any absolute max/min and local max/min for the function f(x)=x^3...
- calculus - Could someone check my reasoning? thanx Find the derivative of the ...
- Please check my Calculus - 1. Which of the following describes the behavior of f...
- Please check my Calculus - 1. Find all points of inflection: f(x)=1/12x^4-2x^2+...
- Math - Find the critical points and the interval on which the given function is ...
- math - can some one please help me with the following questions as i don't ...

More Related Questions