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Question
Find the absolute maximum value and the absolute minimum value of the following function in the given interval:
`f(x) =x^3, x in [-2,2]`
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Solution
f (x) =x3, x ∈ [-2, 2]
= f' (x) = 3x2
For critical points, f' (x) = 0
= 3x2 = 0
= x = 0 ∈ [-2, 2]
Hence, for finding the absolute maximum value and the absolute minimum value, we have to evaluate f (0), f (-2) and f (2).
Now f(0) = 03, f(-2) = (-2)3 = -8 and f (2) = 23 = 8
∴ Absolute maximum value of f (x) = 8 at x = 2 and absolute minimum value of f (x) = -8 at x = -2.
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