Answer
$h(-1)=4, h'(-1)=\frac{1}{2}$
Work Step by Step
$h(-1)=4$ is given, since the problem specifies that the tangent line passes through the point $(-1,4)$ and that $(-1,4)$ is on the graph of $y=h(x)$. Therefore, $h(-1)=4$.
To find $h'(-1)$, find the slope of the tangent line using the other given point $(3,6)$:
$h'(-1)=\frac{6-4}{3-(-1)}=\frac{2}{4}=\frac{1}{2}$
