Question
Asked Apr 26, 2019
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If f(0)= 3 and f '(x) is less than or equal to 3 for all values of x. Use the Mean value Theorem to determine how large f(4) can possibly be. 

f(4) is less than or eqaul to _________  

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Expert Answer

Step 1

The mean value theorem is, if a function is continuous on a closed interval [a, b], where a < b and it is differentiable on the open interval (a, b) than there exists a point c ∈ (a, b) such that,

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Step 2

Since to determine the value of f (4), let take the interval as [0, 4].

Thus, substitute a = 0 and b =4 where f’(x) <=3 for all values of x.

Step 3

Then,  f’(c) <=3 for some c ∈ (0...

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