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21. Let f (x) = (x - 3)-². Show that there is no value of c in (1, 4) such that f (4) - f(1) = f'(c) (4-1). Why does this not contradict the Mean Value Theorem?

21. Let f (x) = (x - 3)-². Show that there is no value of c in (1, 4) such that f (4) - f(1) = f'(c) (4-1). Why does this not contradict the Mean Value Theorem?

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.
Chapter14: Discrete Dynamical Systems
Section14.3: Determining Stability
Problem 1E
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21. Let f (x) = (x - 3)-². Show that there is no value of c in (1,4) such that f (4) f(1) = f'(c) (4-1). Why does this not contradict the Mean Value Theorem? Answer 22. Let f(x) = 2 |2x - 1. Show that there is no value of c such that f (3) f(0) = f'(c) (3-0). Why does this not contradict the Mean Value Theorem? 23-24 Show that the equation has exactly one real solution.
Transcribed Image Text:21. Let f (x) = (x - 3)-². Show that there is no value of c in (1,4) such that f (4) f(1) = f'(c) (4-1). Why does this not contradict the Mean Value Theorem? Answer 22. Let f(x) = 2 |2x - 1. Show that there is no value of c such that f (3) f(0) = f'(c) (3-0). Why does this not contradict the Mean Value Theorem? 23-24 Show that the equation has exactly one real solution.
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