Question

Find the absolute extrema of the following functions on the given closed interval.

f(x) = 3x⁴ – 4x³ ; [– 1, 2]

Answer 1

f(x) = 3x⁴ – 4x³

f'(x) = 12x³ – 12x²

f'(x) = 0

⇒ 12x²(x – 1) = 0

⇒ x = 0 or x = 1

[Here x = 0, 1 ∈ [– 1, 2]]

Now f(–1) = 4

f(0) = 0

f(1) = – 1

f(2) = 16

So absolute maximum = 16 and absolute minimum = – 1