Sketch the graph of a function that satisfies all of the following conditions. Explair • f(0) = 0, and ƒ'(−2) = f'(1) = f'(9) = 0 ● lim f(x) = 0 and lim f(x) =10 x→6 8个8 • f'(x) < 0 on (-∞, -2), (1,6), and (9,∞) • f'(x) > 0 on (-2, 1) and (6,9) • f"(x) > 0 on (-∞, 0) and (12, ∞) • f"(x) < 0 on (0,6) and (6, 12)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15T
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Sketch the graph of a function that satisfies all of the following conditions. Explain!
f(0) = 0, and f'(−2) = f'(1) = f'(9) = 0
● lim f(x) = 0 and lim f(x)
x →∞
x→6
f'(x) < 0 on (-∞, −2), (1,6), and (9, ∞)
ƒ'(x) > 0 on (−2, 1) and (6, 9)
• f"(x) > 0 on (-∞, 0) and (12, ∞)
●
f"(x) < 0 on (0,6) and (6, 12)
●
= ∞
Transcribed Image Text:Sketch the graph of a function that satisfies all of the following conditions. Explain! f(0) = 0, and f'(−2) = f'(1) = f'(9) = 0 ● lim f(x) = 0 and lim f(x) x →∞ x→6 f'(x) < 0 on (-∞, −2), (1,6), and (9, ∞) ƒ'(x) > 0 on (−2, 1) and (6, 9) • f"(x) > 0 on (-∞, 0) and (12, ∞) ● f"(x) < 0 on (0,6) and (6, 12) ● = ∞
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