ConcepTest Section 2.2 Question 1 For Problems 1-2, we want to find how the volume, V, of a balloon changes as it is filled with air. We know V(r) = 4/3.

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Presentation transcript:

ConcepTest Section 2.2 Question 1 For Problems 1-2, we want to find how the volume, V, of a balloon changes as it is filled with air. We know V(r) = 4/3 πr 3, where r is the radius in inches and V(r) is in cubic inches. The expression represents (a) The average rate of change of the radius with respect to the volume when the radius changes from 1 inch to 3 inches. (b) The average rate of change of the radius with respect to the volume when the volume changes from 1 cubic inch to 3 cubic inches. (c) The average rate of change of the volume with respect to the radius when the radius changes from 1 inch to 3 inches. (d) The average rate of change of the volume with respect to the radius when the volume changes from 1 cubic inch to 3 cubic inches.

ConcepTest Section 2.2 Answer 1 ANSWER (c) COMMENT: This is a nice way for students to see the formula and verbal description for average rate of change together.

ConcepTest Section 2.2 Question 2 For Problems 1-2, we want to find how the volume, V, of a balloon changes as it is filled with air. We know V(r) = 4/3 πr 3, where r is the radius in inches and V(r) is in cubic inches. Which of the following represents the rate at which the volume is changing when the radius is 1 inch?

ConcepTest Section 2.2 Answer2 ANSWER (c). Note that (d) would also be a reasonable answer because (a) and (b) provide approximations of the rate of change. COMMENT: Students should be aware that (b) is equivalent to

ConcepTest Section 2.2 Question 3 For the function g(x) shown in Figure 2.3, arrange the following numbers in increasing order. (a) 0 (b) g’(-2) (c) g’(0) (d) g’(1) (e) g’(3)

ConcepTest Section 2.2 Answer 3 ANSWER (c), (d), (a), (b), (e) COMMENT: This can be used as an elimination question in a classroom quiz session.

ConcepTest Section 2.2 Question 4 Which of the following expressions represents the slope of a line drawn between the two points marked in Figure 2.4?

ConcepTest Section 2.2 Answer 4 ANSWER (b) and (e). The coordinates of the two points shown are (a, F(a)) and (b, F(b)), so the slope of the line connecting them is COMMENT: You could repeat this question drawing the graph of a function that was increasing between a and b.

ConcepTest Section 2.2 Question 5 Which of the following expressions represents the slope of a line drawn between the two points marked in Figure 2.5?

ConcepTest Section 2.2 Answer 5 ANSWER COMMENT: You could repeat this question drawing the graph of a function that was decreasing between x and x + ∆x.

ConcepTest Section 2.2 Question 6 Let f(x) = x|x|. Then f(x) is differentiable at x = 0. (a) True (b) False

ConcepTest Section 2.2 Answer 6 ANSWER COMMENT: Students often associate a minus sign with a number less than 0 rather than a number multiplied by – 1.