Question

Let ​ f(x)=x2−3x−4​ .

What is the average rate of change from x = 7 to x = 10?

Answer 1

`14`

EXPLANATION

The given function is

`f(x) = {x}^(2) - 3x - 4`

The average rate of change from x=7 to x=10 is given by;

`(f(10) - f(7))/(10 - 7)`

`f(10) = {(10)}^(2) - 3(10) - 4`

`f(10) = 100 - 30 - 4`

`f(10) = 66`

`f(7) = {7}^(2) - 3(7) - 4`

`f(7) = 49 - 21- 4 = 24`

The average rate of change now becomes:

`(26 - 24)/(3) = (52)/(3) =14`

Answer 2

The average rate of change from x= 7 to x=10 is 14

Explanation:

We can use the slope formula to find the average rate of change

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

Now, we are given f(x) = x^2-3x-4 and x=7 to x=10

Our formula can be rewritten as:

`m=(f(10)-f(7))/(10-7)`

finding f(10) = (10)^2 -3(10) -4

= 100 -30 -4

= 66

and f(7) = (7)^2 -3(7) -4

= 49-21-4

= 24

Now finding m:

m= 66 - 24 / 10-7

m= 42/3

m= 14

So, the average rate of change from x= 7 to x=10 is 14.