Plz help me with this practice

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cjade7660

01.09.2021

Mathematics

$\large\begin{array}{l} \textsf{Hello, Heartrthalhun.}\\\\ \textsf{This is a pretty simple question. Just solve the equation}\\\\\mathsf{f'(x)=0.}\\\\\\ \textsf{The solutions you'll find are the critical values that you're}\\\textsf{looking for.}\\\\ \end{array}$

$\large\begin{array}{l} \mathsf{sin\,2x=0}\\\\ \mathsf{sin\,2x=sin\,0}\\\\ \begin{array}{rcl} \mathsf{2x=0+k\cdot 2\pi}&~\textsf{ or }~&\mathsf{2x=\pi+k\cdot 2\pi}\end{array}\\\\ \begin{array}{rcl} \mathsf{2x=0+k\cdot 2\pi}&~\textsf{ or }~&\mathsf{2x=\pi+k\cdot 2\pi}\end{array}\\\\ \boxed{\begin{array}{rcl}\mathsf{x=k\cdot \pi}&~\textsf{ or }~&\mathsf{x=\dfrac{\pi}{2}+k\cdot \pi} \end{array}}\\\\ \textsf{where k is an integer.} \end{array}$

$\large\begin{array}{l} \textsf{All of those values are critical points.} \end{array}$

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$\large\textsf{I hope it helps.}$

Tags: derivative critical values points function trig trigonometric sine sin solve equation solution differential calculus

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