For a differentiable function

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

For a differentiable function ff, its derivative satisfies • f′(x)>0f'(x)>0 on ( ⁣−∞,−3)(\! -\infty , -3) • f′(x)<0f'(x)<0 on (−3,0)(-3,0) • f′(x)>0f'(x)>0 on (0,4)(0,4) • f′(x)<0f'(x)<0 on (4,∞)(4,\infty) Which of the following gives all intervals on which ff is decreasing? (a) (−∞,−3) and (0,4)(-\infty , -3)\text{ and }(0,4) (b) (−3,0)(-3,0) (c) (−3,0) and (4,∞)(-3,0)\text{ and }(4,\infty) (d) (−∞,−3) and (4,∞)(-\infty , -3)\text{ and }(4,\infty)

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