compute the maximum profit for the profit function P(x)= x^3/3-9/2x^2+8x

Answer 1

as you know, max occurs where P' = 0

P'(x) = x^2 - 9x + 8 = (x-8)(x-1)

Since you know about the general shape of cubic curves, it should be clear which of these values provides a local maximum for P. Naturally, there is no global max for P.

Just plug in x=1 to get P(1)

Answer 2

thank you :) I got it