Determine the possible extreme points of fx 4x3 x4 Then us

Determine the possible extreme points of f(x) = 4x3 - x4. Then use the second derivative test to determine what type of extreme point(s) exist. The possible extreme point(s) is/are .

Solution

df/dx = 12x^2 -4x^3 =0 ; gives extreme points as x=0 , x=3 ; d^2f/dx^2 = 24x-12x^2 ; put x=0 , d^2f/dx^2 =0 put x=3 . d^2f/dx^2 = -36 < 0 (maximum )