MHT CET202613 April 2026Evening ShiftMathematicsApplication of DerivativesActual

Let f(x) be the differentiable function for all x such that f'(x) 5 and f(1) = 4 . The maximum value of f(5) is...

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Correct answer

C. 24

Step-by-step solution

By Lagrange's Mean Value Theorem on the interval [1, 5] , there exists some c (1, 5) such that f'(c) = f(5) - f(1) 5 - 1 Given that f'(x) 5 for all x , we have f'(c) 5 . f(5) - 4 4 5 f(5) - 4 20 f(5) 24 The maximum value of f(5) is 24 . Answer: 24

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