First, we have to find the derivative
[tex]\begin{gathered} h^(\theta)=3cos(\frac{\theta}{2}) \\ \\ h^{\prime}(\theta)=3\frac{d}{d\theta}(cos(\frac{\theta}{2})) \\ h^{\prime}(\theta)=3\text{ \lparen - }\sin(\frac{\theta}{2})\frac{d}{d\theta}(\frac{\theta}{2})) \\ \\ h^{\prime}(\theta)=3(\text{ -}sin(\frac{\theta}{2})(\frac{1}{2}) \\ \\ h^{\prime}(\theta)=\text{ -}\frac{3}{2}sin(\frac{\theta}{2}) \end{gathered}[/tex][tex]\begin{gathered} \text{ - }\frac{3}{2}sin(\frac{\theta}{2})=0 \\ sin(\frac{\theta}{2})=0 \\ \sin^{-1}(0( \\ sin0º=0 \\ andsin180º=0 \\ \\ \\ \end{gathered}[/tex]now he solve for h(theta)
[tex]\begin{gathered} h(\theta)=3cos(\frac{\theta}{2}) \\ \\ h(\text{ -}2\pi)=3cos(\text{ -}\frac{2\pi}{2})=3cos(\text{ -}\pi)=3(\text{ -1\rparen= -3} \\ h(0)=3cos(\frac{0}{2})=3cos0=3(1)=3 \end{gathered}[/tex]