Question

f(x) =  cos x, 0 < x < \[\pi\] .

Answer 1

\[\text { Given: } \hspace{0.167em} f\left( x \right) = \cos x\]

\[ \Rightarrow f'\left( x \right) = - \sin x\]

\[\text { For a local maximum or a local minimum, we must have }\]

\[f'\left( x \right) = 0\]

\[ \Rightarrow - \sin x = 0\]

\[ \Rightarrow \sin x = 0\]

\[ \Rightarrow x = 0 \ or \ \pi\]

Since \[0 < x < \pi\]  none is in the interval \[\left( 0, \pi \right)\] .