Question

Find the average rate of change for f(x) = x2 + 7x + 10 from x = −20 to x = −15. A) −28 B) −36 C) 28 D) 36

Answer 1

Explanation:

Answer 2

The average rate of change of
`f(x)=x^2 + 7x + 10` over the interval
`-20\leq x\leq -15` is -28.

Explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by this expression:

`(f(b)-f(a))/(b-a)`

It is a measure of how much the function changed per unit, on average, over that interval.

To find the average rate of change of
`f(x)=x^2 + 7x + 10` over the interval
`-20\leq x\leq -15` you must:

Evaluate x = -15 and x = -20 into the function f(x)

`f(-15)=(-15)^2 + 7(-15) + 10=130\\f(-20)=(-20)^2 + 7(-20) + 10=270`

Applying the expression for the average rate of change we get

`(f(-15)-f(-20))/(-15+20) \\\\(130-270)/(-15+20) \\\\(-140)/(5)\\\\-28`