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Question
Verify Rolle's theorem for the following function on the indicated interval f(x) = cos 2x on [−π/4, π/4] ?
Solution
The given function is \[f\left( x \right) = \cos2x\].
Since
\[\cos2x\] is everywhere continuous and differentiable, \[\cos2x\] is continuous on
\[ \Rightarrow f'\left( x \right) = - 2\sin2x\]
\[ \Rightarrow - 2\sin2x = 0\]
\[ \Rightarrow \sin2x = 0\]
\[ \Rightarrow \sin2x = 0\]
\[ \Rightarrow x = 0\]
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