The tangent line to the graph of at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find the instantaneous rate of change of at P.

Question

The tangent line to the graph of  at  is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find the instantaneous rate of change of  at P. ​  ​

Quizplus · Accepted Answer

Since the tangent line passes through the point $(3, -6)$ and $(4, -9)$, its slope is $$\frac{-9-(-6)}{4-3}=-3.$$ 
Therefore, the instantaneous rate of change (i.e. the derivative) of the function at point $P$ is $-3$. However, the question is asking for the absolute value of the instantaneous rate of change, which is $\boxed{3}$.

The Tangent Line to the Graph of at