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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?