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Question
f(x) = cos x, 0 < x < \[\pi\] .
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Solution
\[\text { Given: } \hspace{0.167em} f\left( x \right) = \cos x\]
\[ \Rightarrow f'\left( x \right) = - \sin x\]
\[\text { For a local maximum or a local minimum, we must have }\]
\[f'\left( x \right) = 0\]
\[ \Rightarrow - \sin x = 0\]
\[ \Rightarrow \sin x = 0\]
\[ \Rightarrow x = 0 \ or \ \pi\]
Since \[0 < x < \pi\] none is in the interval \[\left( 0, \pi \right)\] .
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