Answer:
or approximately (0.544, 4.179)
Step-by-step explanation:
A function and its tangent lines intersect when their slopes are the same. Find the x-coordinate when the slope of f(x) is equal to 8/7 by taking the derivative of f(x):
Set equal to 8/7 and solve for x:
Therefore, will intersect at a point of tangency with a line of slope 8/7 at x=49/900. Plug in x=49/900 into
to get the y-coordinate:
⇒Answer: (49/900, 3761/900) or approximately (0.544, 4.179)
First of all, a positive average rate of change means that the function is increasing, so the answer can only be A->B or B->C.
The average rate of change is defined as
i.e. as the ratio between the vertical and horizontal gain.
In order to go from point A to point B, you gain 1 unit horizontally and 5 units vertically. So, the average rate of change is 5/1=5.
In order to go from point B to point C, you gain 1 unit horizontally and 3 units vertically. So, the average rate of change is 3/1=3.