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# Verify Lagrange'S Mean Value Theorem for the Following Function: F(X ) = 2 Sin X + Sin 2x " on " [0, Pi] - ISC (Commerce) Class 12 - Mathematics

#### Question

Verify Lagrange's Mean Value Theorem for the following function:

f(x ) = 2 sin x +  sin 2x " on " [0, pi]

#### Solution

f(x) = 2 sin x + sin 2x  " on " [0, pi]

f'(x) = 2cosx + 2cos 2x

1) f(x) is differentiable on [0, pi]

2) Differentibility ⇒ Continuity

:. f(x) is continuous on [0, pi]

∴ LMVT is verified

then there exist c in (0,pi) such that

f'(c) = (f(b) - f(a))/(b-a)

2cos c + 2 cos c = ((2sin pi + sin 2pi) - (2sin 0 +sin 0)) /(pi-0)

2 cos c + 2cos2c = 0

2cos c + 2(2cos^2 c - 1) = 0

2cos^2c + 2cos c -1 = 0

2 cos^2 c +  2 cos c - cos c - 1 = 0

2cos(cos c + 1) -1(cos c + 1) = 0

(cos c + 1)(2cos c - 1) = 0

cos c = -1, cos c = 1/2

c = 0 ∉ (0, pi)

c= pi/3  in  (0, pi)

:. c =pi/3

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 4.1 | 5.00 marks

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Solution Verify Lagrange'S Mean Value Theorem for the Following Function: F(X ) = 2 Sin X + Sin 2x " on " [0, Pi]` Concept: Mean Value Theorem.
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