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Given and f'(-1) = 4 and f(-1) = -6. Find f'(x) and find f(2) = = f"(x) = = 2x + 3

Given and f'(-1) = 4 and f(-1) = -6. Find f'(x) and find f(2) = = f"(x) = = 2x + 3

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.6: Analyzing Graphs Of Functions
Problem 6ECP: Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
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Given and f'(-1) = 4 and f(−1) = −6. Find f'(x) = and find f(2)= ƒ"(x) = 2x + 3
Transcribed Image Text:Given and f'(-1) = 4 and f(−1) = −6. Find f'(x) = and find f(2)= ƒ"(x) = 2x + 3
Problem evaluate the integral: Given that [₁² f(x) dx = 3₁ f² g(x) dx = 2, 3, f(x) — 3g(x) [² — Problem 3. (Definite integrals of odd/even functions.) Consider the integral f(x) dx, ca dx. -a (1) where f is a continuous function and a is any positive number. (a) (5 points) Suppose f(x) is an odd function, i.e., f(-x) = −ƒ(x). Infer the value of the definite integral (1) above by graphing an odd function (anyone you'd like) and using the interpretation of the definite integral as an area. Explain your conclusion briefly in words. (b) (5 points) Suppose f(x) is an even function, i.e., f(-x) = f(x). Write the integral (1) above in terms of f(x) da, again, using a graph for intuition. a
Transcribed Image Text:Problem evaluate the integral: Given that [₁² f(x) dx = 3₁ f² g(x) dx = 2, 3, f(x) — 3g(x) [² — Problem 3. (Definite integrals of odd/even functions.) Consider the integral f(x) dx, ca dx. -a (1) where f is a continuous function and a is any positive number. (a) (5 points) Suppose f(x) is an odd function, i.e., f(-x) = −ƒ(x). Infer the value of the definite integral (1) above by graphing an odd function (anyone you'd like) and using the interpretation of the definite integral as an area. Explain your conclusion briefly in words. (b) (5 points) Suppose f(x) is an even function, i.e., f(-x) = f(x). Write the integral (1) above in terms of f(x) da, again, using a graph for intuition. a
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