Question

Verify Rolles mean value theorem f(x)=2x^3+x^2-4x-2 in [-(2)^1/2,(2)^1/2]​

Answer 1

Answer:

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Step-by-step explanation:

The given function f(x) = 2x3 + x2 - 4x - 2 ...(i) Diff. (i) w.r. to x both sides,

we get f'(x) = 6x2 + 2x - 4 ∴ f'(c) = 6c2 + 2c - 4

By Rolle's Theorems

∴ 6c2 + 2c - 4

= 0 6c2 + 6c - 4c - 4

= 0 6c(c + 1) - 4(c + 1)

= 0 (c + 1)(6c - 4)

= 0

Hence, verified Rolle's theorem