2. Consider a function f that consists of the four line segments joining the points (0,0), (2, -3), (4,5), (6,2) and (8,-2). The function F is defined by the integral F(x) = f(t), dt = [₁ (a) Sketch the graph of f. (b) From your graph and simple geometric formulas, complete the table: 012345678 x F(x) (c) Find the critical numbers for F, the intervals where F is increasing or decreasing, and find all extrema of F on the interval [0,8]. (d) Determine the intervals where F is concave up or concave down, and find all points of inflection of F on the interval (0,8).

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