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71-72. One-sided derivatives The right-sided and left-sided derivatives of a f(a+h) − f(a) h and function at a point a are given by f'+(a) = lim h→0+ f(a+h)-f(a), respectively, provided these limits exist. The f'_(a) = lim h→0- h derivative f'(a) exists if and only if f'+(a) = f'_(a). a. Sketch the following functions. b. Compute f'(a) and f'_(a) at the given point a. c. Is f continuous at a? Is f differentiable at a? 71. f(x) = x - 2|; a = 2 (4-x² 72. f(x) = 2x + 1 if x ≤ 1 ; a = 1 if x > 1'

71-72. One-sided derivatives The right-sided and left-sided derivatives of a f(a+h) − f(a) h and function at a point a are given by f'+(a) = lim h→0+ f(a+h)-f(a), respectively, provided these limits exist. The f'_(a) = lim h→0- h derivative f'(a) exists if and only if f'+(a) = f'_(a). a. Sketch the following functions. b. Compute f'(a) and f'_(a) at the given point a. c. Is f continuous at a? Is f differentiable at a? 71. f(x) = x - 2|; a = 2 (4-x² 72. f(x) = 2x + 1 if x ≤ 1 ; a = 1 if x > 1'

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 48CR
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Question 71? (Show work) answer is given.
71-72. One-sided derivatives The right-sided and left-sided derivatives of a f(a+h)-f(a) and h function at a point a are given by f'+(a) = lim h→0+ f(a+h) − f(a) - f'_(a) = lim h→0- h derivative f'(a) exists if and only if f'+(a) = f'_(a). 9 71. f(x)= x - 2|; a = 2 4- x² 72. f(x) = 2x + 1 respectively, provided these limits exist. The a. Sketch the following functions. b. Compute f'(a) and f'_(a) at the given point a. c. Is f continuous at a? Is f differentiable at a? if x < 1 2 if x > 1 ; a = 1
Transcribed Image Text:71-72. One-sided derivatives The right-sided and left-sided derivatives of a f(a+h)-f(a) and h function at a point a are given by f'+(a) = lim h→0+ f(a+h) − f(a) - f'_(a) = lim h→0- h derivative f'(a) exists if and only if f'+(a) = f'_(a). 9 71. f(x)= x - 2|; a = 2 4- x² 72. f(x) = 2x + 1 respectively, provided these limits exist. The a. Sketch the following functions. b. Compute f'(a) and f'_(a) at the given point a. c. Is f continuous at a? Is f differentiable at a? if x < 1 2 if x > 1 ; a = 1
71.10 b. f' (2) = 1; f'_(2) = -1 c. f is continuous but not differentiable at x = 2.
Transcribed Image Text:71.10 b. f' (2) = 1; f'_(2) = -1 c. f is continuous but not differentiable at x = 2.
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