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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

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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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