Let be a differentiable function whose derivative is given by f'(x)=(x-2)(x+1)(x-5)

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let ff be a differentiable function whose derivative is given by f′(x)=(x−2)(x+1)(x−5).f'(x)=(x-2)(x+1)(x-5). Which of the following lists all intervals on which ff is increasing? (a) (−∞,−1) and (2,5)(-\infty,-1) \text{ and } (2,5) (b) (−∞,−1) and (2,∞)(-\infty,-1) \text{ and } (2,\infty) (c) (−1,2) and (5,∞)(-1,2) \text{ and } (5,\infty) (d) (−∞,−1),(−1,2), and (5,∞)(-\infty,-1), (-1,2), \text{ and } (5,\infty)

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