Question

Find the average rate of change for f(x) = x2 + 7x + 10 from x = −20 to x = −15.

Answer 1

Explanation:

This is a parabola. The only way you could find the actual rate of change at those x values is by finding the instantaneous rate of change at each of those points which requires calculus. The average rate of change is found when you find the slope of the line between the 2 points (-20, y) and (-15, y). To find y in each case, sub in the x values and solve for y:

`f(-20)=(-20)^2+7(-20)+10` and

f(-20) = 270 and the resulting coordinate is (-20, 270).

Likewise for f(-15):

`f(-15)=(-15)^2+7(-15)+10` and

f(-15) = 130 and the resulting coordinate is (-15, 130)

Applying the slope formula now will find the average rate of change between those 2 points:

`m=(130-270)/(-15-(-20))` which simplifies to

`m=(-140)/(5)` so

m = -28