# Thread: Maximum profit - Calculus (urgent!)

1. ## Maximum profit - Calculus (urgent!)

If profit is given by:

p(x) = 280x - 3x^3 + 5x ln(x)

The average profit form would be:
= p(x) / x

= 280 - 3x^2 + 5 ln(x)
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now, how do i determine how many units should be produced so the average profit is a max ?!

2. I'd really appreciate it if anyone can tell of if I'm on the right track!

For a maximum point, f'(x) = 0 and f"(x) < 0

Therefore:
We find the first and the 2nd derivate of the AVERAGE profit function:

P'(x) = - 6x + 1/x = 0
P"(x) = [ -6 - 1/x^2 ] < 0

IS this right so far?!!

I'm really confused.