Question

Verify the Rolle’s Theorem for the function f(x) = sin 2x in [0,π] *

Answer 1

Step-by-step explanation:

f(x)=sin2x in [0,π] is continuous

f(x)=sin2x is differentiable in(a,b) becoz there is no sharp edge in sin2x curve

f(0)=f(π)

then there exist a mean value belongs to (a,b) such that. f'(c)=0.

Answer 2

Answer:

According to the Rolle's theorem  ,

   f(x) = sin x - sin 2x in (0 , $\pi$ )

f(c) = f($\pi$) - f(0)/$\pi$ - 0

2 cos c - 2 cos 2c = sin$\pi$ - 2sin$\pi$ - sin0 + sin0 / $\pi$ - 0

2 cos 2c - cos c = 0

2 ( 2cos∧2 c - 1 ) - cos c = 0

4cos∧2 c - cos c - 2 = 0

cos c = $1+-\sqrt{1+32}$ / 8

cos c = 1+- √33 / 8

c = cos∧-1 ( 1+-√33 / 8 )

c = ( 0 , $\pi$ )

Step-by-step explanation:

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