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

f(x) = x3+x2 - 6x on [-1, 4]

1 Answer

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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 [-1,4].

= 10

f' (c) = 3c2+2c - 6

⇒ 3 c2+2c - 6 = 10

⇒ 3 c2+2c - 16 = 0

⇒ 3 c- 6c+8c - 16 = 0

⇒ 3c(c - 2)+8(c - 2) = 0

⇒ (3c+8)(c - 2) = 0

c = 2, -8/3

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