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If f'(x) = (x – 1) (x – 2) (x – 3) then f(x) in monotonically increasing in (a) x < 1 (b) x > 3, x < 1 (c) x > 3, 1 < x < 2 (d) x < 1, 2 < x < 3

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 If f'(x) = (x – 1) (x – 2) (x – 3) then f(x) in monotonically increasing in 

(a) x < 1 (b) x > 3, x < 1 (c) x > 3, 1 < x < 2 (d) x < 1, 2 < x < 3

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Correct option (c)

Explanation:

When x > 3, f '(x) > 0; when 2 < x < 3, f '(x) < 0; when 1 < x < 2, f '(x) > 0; when x < 1, f '(x) < 0.

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