Find the absolute maximum and absolute minimum of the function f(x)=3x2-x3 on [0,∞)

Question

Find the absolute maximum and absolute minimum of the function f(x)=3x²-x³ on [0,∞)

Answer 1

Make a graph! Then differentiate f and set the derivative = 0.

It has no absolute minimum, i.e. f goes to -∞ as x gets large

The local and absolute maximum on the specified interval occurs at x=2 and is 4.