There is a garden of apples and the profit from a garden of apple trees is given by

Question

f( x ) = 70 + 30 x^2 - (1/3) x^3,
where x = number of apples trees per acre. How many trees per acre will maximize the profit?

Answer 1

f'(x) = 60x-x^2 = x(60-x)
so, max profit when x=60

Answer 2

Solution:
max{70+30 x^2-x^3/3} = 36070
is at x = 60