Determine the possible extreme points of fx 12x3x4 Then use

Determine the possible extreme points of f(x) = 12x3-x4. Then use the second derivative test to determine what type of extreme point(s) exist. The possible extreme point(s) is/are .

Solution

f\'=36x^2-4x^3=0 x=0 x=9 f\'\'=72x-12x^2 x=0 f\'\'=0 so neithre min nor max exists at x=0 x=9 f\'\'=-324 <0 hence max exists at x=9 and value is=2187