Consider the function y = f(x) graphed below, and let F(x) denote the antideriva

Question

Consider the function y = f(x) graphed below, and let F(x) denote the antiderivative of f(x). You may assume that f(x) as roots at x = - 11/3, - 1, 1, and 11/3 You may also assume that x = -8/3 and 8/3 are local minima for f(x). On what interval(s) is F(x) decreasing? What are the critical points of Fix)? Fix) appears to have three inflection points. What are they? On what interval(s) is Fix) concave down? Make a sketch of F(x) directly on the graph above assuming that F(0) = 0. Consider the piecewise-linear function y = f(x) graphed below. Let F(x) denote the antiderivative of y = f(x) on the interval [0, 6]. Assume that F(0) = 0. Using the Fundamental Theorem of Calculus, fill out the table below. As carefully as you can, draw a graph of F(x) on the blank coordinate system below.

Explanation / Answer

1

a) F(x) is decreasing in (-11/3,-1)U(1,11/3)

b) Critical points are -11/3, -1, 1, 11/3

c) Points of inflection -8/3,0,8/3

d) (-inf, -11/3) U (-1, 1)

2

x 0 1 2 3 4 5 6 F(x) 0 1/2 3/2 5/2 3 5/2 2

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