1. * () Fill in the blanks in the following table: f is concave up on (a, b) f is concave down on (a, b) f' is on (a, b) f' is on (a, b) f" is on (a, b) f" is on (a, b) 2. * (5-3) All three parts of this problem refer to the following graph: B E G (a) * (5) Assume that the graph is a graph of the function f. On approximately what interval(s) is f concave up? On approximately what interval(s) is f concave down? At what r-values does f change concavity ? (b) * (5) Now assume that the graph is a graph of the function f'. This time, on what interval(s) is f concave up, and on what interval(s) is f concave down? At what r-values does f change concavity? (Hint: Use the second row of the table above.) (c) * () Now assume that the graph is a graph of the function f". On what inter- val(s) is f concave up? On what interval(s) is f concave down? At what a-values does f change concavity? (Hint: Use the third row of the table above.) "In other words, at what a-values does f go from concave up to concave down or vice versa? People refer to the r-values where concavity changes as inflection points; I am deliberately avoiding using this term in class 5. * () Determine the intervals on which the function is concave up or down and find the r-values where concavity changes. (a) *(5) f(x) = 2x3 - 7x2+5 (b) * (5) f(x) = x(x - 9VI), 1 > 0 (c) *( 5) f(x) = 21 (d) f(x) = 3x + sin(3x), r E [0, ] 7. *() Find the x-values for which the functions f below change concavity or show that no such r-values exist. (a) * f(x) = 2x3 - 7x2 +5 (b) * f(x) = 2 Figure 2: graph of y = f'(x) y =f'(x) 2- (c) * f(x) = 3x3 - 1x2 -2r + 3 (d) * f(x) = x7 - 25