Question

Let ​ f(x)=x2−3x−4​ .

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

Answer 1

Answer:

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

Step-by-step explanation:

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

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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

Our formula can be rewritten as:

$m=\frac{f(10)-f(7)}{10-7}$

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.

Answer 2

ANSWER

$14$

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;

$\frac{f(10) - f(7)}{10 - 7}$

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

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

$f(10) = 66$

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

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

The average rate of change now becomes:

$\frac{26 - 24}{3} = \frac{52}{3} =14$