Question

Unit Test Unit Test Active 1 2 3 4 5 6 7 CO Given fix) = 17- x2, what is the average rate of change in f(x) over the interval [1, 5]? -6, -1/2, 1/4, 1​

Answer 1

Explanation:

Average rate of change is the same thing as the slope. This is a quadratic so the slope is not something that is constant like it is in a line. Here you have the x coordinates of 1 and 5; each one of these x coordinates has a y coordinate that goes with it. If we draw a line from one of these coordinates to another, that line will have a slope. That is the slope we are trying to find. Thus, we need the y coordinates that go with each of these x coordinates. To do that, plug x into the equation and do the math to find y:

Let's start with x = 1.

f(1) =
`17-(1)^2` so

f(1) = 16 and the coordinate is (1, 16).

f(5) =
`17-(5)^2` so

f(5) = -8 and the coordinate is (5, -8). Now we apply the slope formula:

`m=(-8-16)/(5-1)=(-24)/(4)=-6` So the answer is -6.