The tangent line to the graph of f (x) 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 f (x) at P.
A) -3
B) 2
C) 1
D) -4
E) does not exist

Question

The tangent line to the graph of f (x) 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 f (x) at P. ​  ​
A) -3 
B) 2 
C) 1 
D) -4 
E) does not exist

Quizplus · Accepted Answer

To find the instantaneous rate of change of f(x) at point P, we need to find the slope of the tangent line at P.

From the graph, we can see that point A has coordinates (9,-1) and point P has coordinates (10,0). Therefore, the slope of the line passing through points A and P is:

slope = (0-(-1))/(10-9) = 1

Since the tangent line at P is parallel to this line, it has the same slope of 1. Therefore, the instantaneous rate of change of f(x) at P is 1.

Therefore, the correct answer is B).

The Tangent Line to the Graph of F (X) at