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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 For The Life Sciences
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.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 21CR
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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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