Let $f(x)=8secx.$

$($a$)(1$ point$)$ Find $f^{\text{'}}(x).$

$($c$)(2$ points$)$ Carefully sketch and label $f$ and $f^{\text{'}}$ over $-\frac{}{2},\frac{}{2}$ on the same set of axes below.

$($b$)(3$ points$)$ Find the coordinates of the points with $-\frac{}{2}x\frac{}{2}$ on $f$ where the line tangent to $f$ is parallel to $y=4.$

$($d$)(3$ points$)$ Prove that there exists a solution to the equation

$f(x)=9$

$.$

in $0,\frac{}{3}.$ Its a three part question