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Reconstruct a decreasing function with an isolated zero gradient

The diagram shows y=f′(x)y=f^{\prime}(x) meeting the x-axis at x=−3x=-3 and x=1x=1. Given f(−3)=4f(-3)=4 and f(1)=1f(1)=1:

(i) State the coordinates and natures of the stationary points of y=f(x)y=f(x). marks

(ii) Find the range of xx for which the curve is strictly decreasing. marks

(iii) Sketch y=f(x)y=f(x). marks

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Given derivative is negative before −3, touches zero at −3 as a local maximum, falls to an unlabelled negative minimum, then rises and crosses the axis at 1. It is positive after 1.
Given derivative is negative before −3, touches zero at −3 as a local maximum, falls to an unlabelled negative minimum, then rises and crosses the axis at 1. It is positive after 1.
Given derivative is negative before −3, touches zero at −3 as a local maximum, falls to an unlabelled negative minimum, then rises and crosses the axis at 1. It is positive after 1.

[2010/TPJC/I/6]

CJC · Review problems · Question 5

Separate f′<0 from the definition of a strictly decreasing function.

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