#### Question

Verify Mean Value Theorem, if f (x) = x^{3} – 5x^{2} – 3x in the interval [a, b], where a = 1 and b = 3. Find all c ∈ (1, 3) for which f ′(c) = 0.

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#### Solution

The given function *f* is f (x) = x^{3} – 5x^{2} – 3x

*f*, being a polynomial function, is continuous in [1, 3] and is differentiable in (1, 3) whose derivative is 3*x*^{2} − 10*x* − 3.

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Solution for question: Verify Mean Value Theorem, If F (X) = X3 – 5x2 – 3x in the Interval [A, B], Where a = 1 and B = 3. Find All C ∈ (1, 3) for Which F ′(C) = 0. concept: null - Mean Value Theorem. For the courses CBSE (Commerce), CBSE (Science), CBSE (Arts)