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Verify Lagrange’s mean-value theorem for the following function:

f(x) = x2+x - 1 on [0, 4]

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Best answer

Given:

Since the f(x) is a polynomial function,

It is continuous as well as differentiable in the interval [0,4].

= 5

⇒ f'(c) = 2c+1

⇒ 2c+1 = 5

⇒ c = 2

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