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प्रश्न
Find the absolute extrema of the following functions on the given closed interval.
f(x) = 3x4 – 4x3 ; [– 1, 2]
उत्तर
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
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