Question

What is the average rate of change for ƒ(x) = −4x + 40 over the interval 1 ≤ x ≤ 3?

Answer 1

Answer:

The average rate of change is = - 4

Step-by-step explanation:

If y = f(x) is a function then the average rate of change for f(x) between the interval a ≤ x ≤ b is given by

$\frac{f(b) - f(a)}{b - a}$.

Now, in this case the function is given by f(x) = - 4x + 40 and the interval is 1 ≤ x ≤ 3.

Therefore, f(1) = - 4(1) + 40 = 36 and f(3) = - 4(3) + 40 = 28

So, the average rate of change is = $\frac{28 - 36}{3 - 1} = - \frac{8}{2} = - 4$ (Answer)

Answer 2

Answer:

−30

Step-by-step explanation:

−30 is the average rate of change for ƒ(x) = −4x + 40 over the interval 1 ≤ x ≤ 3.

ƒ(b) − ƒ(a)

b − a

=  ƒ(3) − ƒ(1)

3 − 1

=  −24 − 36

2

=  −60

2

= −30