## Calculus 10th Edition

$g(4)=5, g'(4)=-\frac{5}{3}$
$g(4)=5$ is given, since the problem specifies that the tangent line passes through the point $(4,5)$ and that $(4,5)$ is on the graph of $y=g(x)$. Therefore, $g(4)=5$. To find $g'(4)$, find the slope of the tangent line using the other given point $(7,0)$: $g'(4)=\frac{0-5}{7-4}=-\frac{5}{3}$