Question

Suppose that the profit P obtained in selling x units of a certain item each week is

given by

p=50 √ 3 - 0.5-500(0<x<8000)

.

Find the rate of change of P with respect to x when x=1600.

Answer 1

$$p(x)=50\sqrt{3}x^2 - 0.5x-500$$

$$p'(x)=100\sqrt{3}x-0.5$$

$$p'(1600)=100\sqrt{3}(1600)-0.5$$

$$=160000\sqrt{3}-0.5$$