Finding the minimum perimeter.

[Precepts]

Homework Statement

I'm stuck on part b) of the question, but this includes the whole thing:

A farmer wants to make a rectangular paddock with an area of 4000m^2. However, fencing costs are high and she wants the paddock to have a minimum perimeter.

a) Show that the perimeter is given by the equation P = 2x + 8000/x

b) Find the dimensions of the rectangle that will give the minimum perimeter, correct to 1 decimal place.

The Attempt at a Solution

a) A = 4000 = xy

y = 4000/x

P = 2x + 2y
= 2x + 2(4000/x)
= 2x + 8000/x

Okay, so that was easy.

b) I assume here I just find the first derivative of P (to find minima)

dP/dx = 2 + 8000/x^2

So; 8000/x^2 + 2 = 0

Obviously this won't solve because I can't find x ( negative sq. root)... Where have I gone wrong exactly?

 

[grzz]

The derivative wrt x of $\frac{1}{x}$ ie of x$^{-1}$ = -x$^{-2}$= -$\frac{1}{x^{2}}$

 

[Precepts]

The derivative wrt x of $\frac{1}{x}$ ie of x$^{-1}$ = -x$^{-2}$= -$\frac{1}{x^{2}}$

So I should do P = 2x + 8000x^-1 instead... So x isn't on the bottom?

Can you show me the solution?edit - Nvm, simple mistake with the derivative.

 

[grzz]

Yes you just had a simple mistake with the derivative.

Just replace the + with a - on the RHS of your derivative.