(5) Prove that if f is continuously differentiable on [a, b], then |f(a) – f(b)| a – b max f'(x)| rE[a,b) You'll probably want to use a theorem from Calc I. Also, why can I say max here, instead of sup?
(5) Prove that if f is continuously differentiable on [a, b], then |f(a) – f(b)| a – b max f'(x)| rE[a,b) You'll probably want to use a theorem from Calc I. Also, why can I say max here, instead of sup?
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.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 33E
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![(5) Prove that if f is continuously differentiable on [a, b], then
| F(a) – f(b)|
max f'(x)|
rE[a,b)
a – b
You'll probably want to use a theorem from Calc I. Also, why can I say max here, instead
of sup?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfb88d8d-6f1d-4d74-ab06-2e6bd89a8e95%2Fca7831dd-fadf-405a-bd65-24b4db3788a3%2Fiw0w52g_processed.png&w=3840&q=75)
Transcribed Image Text:(5) Prove that if f is continuously differentiable on [a, b], then
| F(a) – f(b)|
max f'(x)|
rE[a,b)
a – b
You'll probably want to use a theorem from Calc I. Also, why can I say max here, instead
of sup?
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