Differentiability: Mean Value Theorem - Maximum
is a function that is continuous and differentiable in the domain . If and for all , what is the maximum possible value of
The answer is 133.
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1 solution
Using mean value theorem, we have 1 4 ≥ f ( x ) = 1 5 − 7 f ( 1 5 ) − f ( 7 ) = 8 f ( 1 5 ) − 2 1 .
Simplifying this gives f ( 1 5 ) ≤ 1 3 3 .