Choose the correct alternative. If f(x) = 3x3 - 9x2 - 27x + 15 then

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f has maxima at x = –1 Explanation: f(x) = 3x3 - 9x2 - 27x + 15 ∴ f'(x) = 9x2 - 18x - 27 ∴ f''(x) = 18x - 18 Consider, f '(x) = 0 ∴ 9x2 - 18x - 27 = 0 ∴ x2 - 2x- 3 = 0 ∴ (x – 3) (x + 1) = 0 ∴ x = 3 or x = – 1 For x = 3, f ''(x) = 18(3) – 18 = 36 > 0 ∴ f(x) has minimum value at x = 3 ∴ Minimum value = f(3) = – 66 For x = – 1, f ''(x) = 18(–1) – 18 = – 36 < 0 ∴ f(x) has maximum value at x = –1 ∴ Maximum value = f(–1) = 30.

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