Rolle's/MVT Problem Need some help

Loppyfoot

1. The problem statement, all variables and given/known data
Does the function f exist when f(0)=-1, f(2)=4, and f'(x)≤2 for all values of x? Justify your answer.

3. The attempt at a solution
I am having some trouble with where to start...and end. Thanks for your help.

Dick

Homework Helper
What would the mean value theorem tell you about f(x) on the interval [0,2]?

Loppyfoot

What would the mean value theorem tell you about f(x) on the interval [0,2]?
It tells me that there exists a number c in (0,2) such that f'(c) = (f(2)-f(0))/(2-0)

Dick

Homework Helper
Ok. What is (f(2)-f(0))/(2-0) as a number?

Loppyfoot

so 2.5 is not less than or equal to 2, so the function would not exist?

Dick

Homework Helper
so 2.5 is not less than or equal to 2, so the function would not exist?
Exactly.

Loppyfoot

Great. Thank you, Sir.

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