Determine the maximum value of y = 3×2 – x3

Explanation

y = 3x² - x³
dy/dx = 6x - 3x²
as dy/dx = 0
6x - 3x² = 0
3x (2 - x) = 0
this implies that 2 -x = 0 and 3x = 0
x = 2 (or) 0
But = dy/dx = 6x - 3x²
d²y/dx² = 6 - 6x at x = 2
= 6 - 6(2)
= -6
y = 3x² - x³
= 3(2)² - 2³
= 12 - 8
= 4