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The figure below shows the graph of f ', the derivative of the function f, on the closed interval from x = -2 to x = 6. The graph of the derivative has horizontal tangent lines at x = 2 and x = 4.

Find the x-value where f attains its absolute maximum value on the closed interval from x = -2 to x = 6.

The figure below shows the graph of f the derivative of the function f on the closed interval from x 2 to x 6 The graph of the derivative has horizontal tangen class=

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MathPhys

Answer:

x = -2

Step-by-step explanation:

From x = -2 to x = 5, f' is negative.  That means f is decreasing.

From x = 5 to x = 6, f' is positive.  That means f is increasing.

The negative area (between x = -2 and x = 5) is larger than the positive area area (between x = 5 and x = 6).  That means f decreases more than it increases.

So f is an absolute maximum at x = -2.