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Verify Lagrange’s mean value theorem for the following functions:

f(x) = 2x – x2, x ∈ [0, 1].

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The function f given as f(x) = 2x – x2 is a polynomial function.

Hence, it is continuous on [0, 1] and differentiable on (0, 1). 

Thus, the function f satisfies the conditions of Lagrange’s mean value theorem.

∴ there exists c ∈ (0, 1) such that

Hence, Lagrange’s mean value theorem is verified.

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