#### Question

f(x) = cos x, 0<x< \[\pi\] .

#### 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 \[\left( 0, \pi \right)\] .

Is there an error in this question or solution?

Solution F(X) = Cos X, 0<X< π . Concept: Graph of Maxima and Minima.