Refer to Fig. 1.(a) Looking at the graph of f′(x), determine whether f(x) is increasing or...

Refer to Fig. 1.

(a) Looking at the graph of f′(x), determine whether f(x) is increasing or decreasing at x = 9. Look at the graph of f(x) to confirm your answer.

Figure 1

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(b) Looking at the values of f′(x) for 1 ≤ x<2 and 2 < x ≤ 3, explain why the graph of f(x) must have a relative maximum at x = 2. What are the coordinates of the relative maximum point?

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(c) Looking at the values of f′(x) for x close to 10, explain why the graph of f(x) has a relative minimum at x = 10.

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(d) Looking at the graph of f″(x), determine whether f(x) is concave up or concave down at x = 2. Look at the graph of f(x) to confirm your answer.

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(e) Looking at the graph of f″(x), determine where f(x) has an inflection point. Look at the graph of f(x) to confirm your answer. What are the coordinates of the inflection point?

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(f ) Find the x-coordinate of the point on the graph off(x) at which f(x) is increasing at the rate of 6 units per unit change in x.