The graph of the derivative f' of a continuous function f is shown below. (Assume f' continues to co.) y = f'(x) (a) On what interval(s) is fincreasing? (Enter your answer using interval notation.) (0, 2) U ( 4, 6) U (8, + ∞) On what interval(s) is f decreasing? (Enter your answer using interval notation.) (2, 4) U (6, 8) (b) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.) X = At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.) X = (c) On what interval(s) is f concave upward? (Enter your answer using interval notation.) On what interval(s) is f concave downward? (Enter vour answer using interval notation.)
The graph of the derivative f' of a continuous function f is shown below. (Assume f' continues to co.) y = f'(x) (a) On what interval(s) is fincreasing? (Enter your answer using interval notation.) (0, 2) U ( 4, 6) U (8, + ∞) On what interval(s) is f decreasing? (Enter your answer using interval notation.) (2, 4) U (6, 8) (b) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.) X = At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.) X = (c) On what interval(s) is f concave upward? (Enter your answer using interval notation.) On what interval(s) is f concave downward? (Enter vour answer using interval notation.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter4: Calculating The Derivative
Section4.2: Derivatives Of Products And Quotients
Problem 35E
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Question
Transcribed Image Text:The graph of the derivative f' of a continuous function f is shown below. (Assume f' continues to o.)
y= f'(x)
(a) On what interval(s) is fincreasing? (Enter your answer using interval notation.)
(0, 2) U (4, 6) U (8, + x)
On what interval(s) is f decreasing? (Enter your answer using interval notation.)
(2, 4) U (6, 8)
(b) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.)
X =
At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.)
X =
(c) On what interval(s) is f concave upward? (Enter your answer using interval notation.)
On what interval(s) is f concave downward? (Enter your answer using interval notation.)
(d) State the x-coordinate(s) of the point(s) of inflection. (Enter your answers as a comma-separated list.)
X =
(e) Assuming that f(0) = 0, sketch a graph of f.
y
10
10-
8
8
6
6
4
4
2
X.
10
2
4
8
10
4
8
y
y
10-
10
8
6
4
4
2
2
4
6
8
10
2
4
6
8
10
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