Rolle's/MVT Problem Need some help

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

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

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Ok. What is (f(2)-f(0))/(2-0) as a number?
 
so 2.5 is not less than or equal to 2, so the function would not exist?
 

Dick

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Great. Thank you, Sir.
 

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