Posted by **sammy** on Thursday, October 5, 2006 at 8:14am.

given S=piX(X+2Y) and V=piX^2Y show that dS/dX=pi(X-Y) when V is constant, and

dV/dX=-piX(X-Y)when S is constant.

Please HELP!!

I have tried several times, and I dont get the result you asked for.

If we're given S=piX(X+2Y), then

dS/dx= piX(1+2Y')+pi(X+2Y)=

pi(X+2XY'+X+2Y) or

(1) dS/dx = 2pi(X+Y+XY')

We're also told V=piX^2Y so

dV/dx=piX^2Y' + 2piXY or

(2) dV/dx = piX(XY'+2Y)

(You should recognize these as the surface and volume formulas for a right circular cylinder.)

When V is constant (2) is 0, so XY'+2Y=0 or Y'=-2Y/X. Using this for Y' in (1) we get

dS/dx = 2pi(X+Y+X(-2Y/X))=2pi(X-Y)

Are you missing a 2 or did I accidentally add one, check to see if this is correct. Also note that the result holds when X>0, for X=0 the result is trivial.

You should be able to do a similar calculation when dS/dx = 0, solve for Y' and substitute into dV/dx.

## Answer this Question

## Related Questions

- Calc BC - 1. Find the indefinite integral. Indefinite integral tan^3(pix/7)sec^2...
- calculus - find the derivative of y=cos pix/sinpix+cospix
- trig - determine the amplitude,period and phase shift of y=-2cos(pix-3)
- Math- Calculus - Locate the absolute extrema of the function on the closed ...
- pre cal - what is the period of these functions y=1/2 cos 3pi/2 y=2 cos piX/2
- pre cal - what is the period of these functions y=1/2 cos 3pi/2 y=2 cos piX/2
- pre cal - what is the period of these functions y=1/2 cos 3pi/2 y=2 cos piX/2
- Math - What is the derivative of: y = sin(1)sin^2(x^4)+sec^2(pix^2+x+1)
- calculus - The volume of a solid is given by V=pi x^2(lnx)^2. what is the ...
- Calculus - Suppose f(x)=2x^2-x^3 and g(x)= sin(pix/2). a) What is the exact ...