The Image Of The Interval [–1, 3] Under The Maping f(x) = 4x3 – 12x is.

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Question

The image of the interval [–1, 3] under the maping f(x) = 4x³ – 12x is.

easy

Solution

Correct option is

[–8, 72]

To find the image of the given interval, we must find the set of value of f (x) for x ∈ [–1, 3]. By virtue of the continuity of f (x), the image is the interval

The critical points of f (x) are given by f ‘ (x) = 12 x ² – 12 = 12(x ² – 1) = 0.

That is, x = ±1, so that f (1) = 4. 1 – 12 = –8, f (–1)

= –4 + 12 = 8 and f (3) = 4. 27 – 12. 3 = 108 – 36 = 72.

Hence the image of [–1, 3] under the mapping f (x) is [–8, 72].