(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?

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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?
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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