Find absolute maximum and minimum values of a function f given by f(x) = 12x 4/3 – 6x 1/3 , x ∈ [–1, 1].

Question

Philoid · Accepted Answer

We have,

f(x) =

f’(x) =

Thus, f’(x) = 0

⇒ x =

Further note that f’(x) is not define at x = 0.

So, the critical points are x = 0 and x = and at the end point of the interval x = – 1 and x = 1

f(– 1) =

f(0) =

f() =

f(1) =

Thus, we conclude that the absolute maximum value of f is 18 at x = 1, and absolute minimum value of f is which occurs at x = .