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Read stationary points from a derivative graph

The derivative graph y=f′(x)y=f^{\prime}(x) is shown. Find the x-coordinates of the stationary points of f(x)f(x) and determine their nature.

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Illustrative upward-opening derivative graph with zeros 0 and 2, positive outside(0,2), negative inside. Vertical scale is illustrative; no exact derivative formula is asserted.
Illustrative upward-opening derivative graph with zeros 0 and 2, positive outside(0,2), negative inside. Vertical scale is illustrative; no exact derivative formula is asserted.
Illustrative upward-opening derivative graph with zeros 0 and 2, positive outside(0,2), negative inside. Vertical scale is illustrative; no exact derivative formula is asserted.

CJC · Lecture · Example 3

Identify whether the given curve is a function, an implicit relation or a derivative graph before choosing the test.

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