If the tangent line to $y = f ( x )$ at $( 8,4 )$ passes through the point $( 4 , - 32 )$, find $f ^ { \prime } ( 8 )$. Select the correct answer.
A) $f ^ { \prime } ( 8 ) = 29$
B) $f ^ { \prime } ( 8 ) = 19$
C) $f ^ { \prime } ( 8 ) = 9$
D) $f ^ { \prime } ( 8 ) = 34$
E) $f ^ { \prime } ( 8 ) = - 9$

Question

Quizplus · Accepted Answer

The slope of the tangent line is the derivative at that point. Using the slope formula $(y_2 - y_1)/(x_2 - x_1)$, the slope between $(8, 4)$ and $(4, -32)$ is $(-32 - 4)/(4 - 8) = -36/-4 = 9$. Thus, $f'(8) = 9$.

If the Tangent Line To y=f(x)y = f ( x )y=f(x)

If the Tangent Line To $y = f ( x )$