. (a) Continuous for all real numbers (b) f'(x) > 0 on (-0, -2) and (0, 3) (c) f'(x) < 0 on (-2, 0) and (3, 0) (d) f"(x) < 0 on (-x, 0) and (0, 5) (e) f"(x) > 0 on (5, 0) () f'(-2) = f'(3) = 0 (g) f'(0) doesn't exist (h) Differentiable everywhere except at x = 0 (i) An inflection point at (5, 1)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Sketch the graph of a single function that has all of the properties listed.

. (a) Continuous for all real numbers
(b) f'(x) > 0 on (-0, -2) and (0, 3)
(c) f'(x) < 0 on (-2, 0) and (3, 0)
(d) f"(x) < 0 on (-x, 0) and (0, 5)
(e) f"(x) > 0 on (5, 0)
() f'(-2) = f'(3) = 0
(g) f'(0) doesn't exist
(h) Differentiable everywhere except at x = 0
(i) An inflection point at (5, 1)
Transcribed Image Text:. (a) Continuous for all real numbers (b) f'(x) > 0 on (-0, -2) and (0, 3) (c) f'(x) < 0 on (-2, 0) and (3, 0) (d) f"(x) < 0 on (-x, 0) and (0, 5) (e) f"(x) > 0 on (5, 0) () f'(-2) = f'(3) = 0 (g) f'(0) doesn't exist (h) Differentiable everywhere except at x = 0 (i) An inflection point at (5, 1)
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