SOLUTION: Hi I keep doing something wrong in this problem. Can you help me solve it? thanks A function is given below. Determine the average rate of change of the function between x = -4

Algebra ->  Equations -> SOLUTION: Hi I keep doing something wrong in this problem. Can you help me solve it? thanks A function is given below. Determine the average rate of change of the function between x = -4       Log On


   

Question 126975: Hi I keep doing something wrong in this problem. Can you help me solve it? thanks
A function is given below. Determine the average rate of change of the function between x = -4 and x = 1.
h(t) = t^2 - 10t
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The average rate of change of f(x) between x = a and x = b is given by the slope of the line that passes through the points (a, f(a)) and (b, f(b)) (called a secant line). Given two points, you can calculate a slope using the formula:

m=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29, so for the slope of the described secant line:

%28f%28a%29-f%28b%29%29%2F%28a-b%29

For your function:

a+=+-4, so f%28a%29=f%28-4%29=%28-4%29%5E2-10%28-4%29=16%2B40=56

b=+1, so f%28b%29=f%281%29=%281%29%5E2-10%281%29=1-10=-9

%28f%28a%29-f%28b%29%29%2F%28a-b%29=%2856-%28-9%29%29%2F%28-4-1%29=65%2F-5=-13

Let's draw a picture and see if the answer makes sense:



The secant line pictured doesn't look as steep as it should be for a -13 slope, but that is because I have different scales for the x and y axis so that you can actually see something. But the intersection points look correct and the configuration of the parabola is right (vertex at (5,-25), zeros at 0 and 10, concave up, etc.)