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The absolute maximum value of the function $f (x) = 2 x^{3} - 3 x^{2} - 36 x + 9$ defined on [-3, 3] is

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answer is B.

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Detailed Solution

$f (x) {= 2x}^{3} {- 3x}^{2} -36x + 9$

$f^{1} (x) {= 6x}^{2} - 6x - 36$

$f^{1} (x) = 0 \Rightarrow x^{2} -x-6 = 0$

x = -2, 3

Maximum value = f(-2) = 53

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