Correct Answer: Option D

Explanation

f(x) = x\(^3\) - 12x + 11

\(\frac{df(x)}{dx)}\) = 3x\(^2\) - 12 = 0

∴ 3x\(^2\) - 12 = 0 \(\to\) x\(^2\) = 4

x = \(\pm\)2, f(+2) = 8 - 24 + 11 = -15

= f(-2) = (-8) + 24 + 11

= 35 - 8 = 27

∴ maximum value = 27

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