Question

What is the average rate of change of f(x)=x2+x−6 between x=1 and x=3 ?

A
5

B
–5

C
15

D
10

Answer 1

The average rate of change of f(x) = x^2 + x - 6 between x = 1 and x = 3 is 6.5.

Step-by-step explanation:

To find the average rate of change of the function f(x) = x^2 + x - 6 between x = 1 and x = 3, we need to calculate the difference in the function values and divide it by the difference in x values.

First, we evaluate the function at x = 1 and x = 3:

f(1) = 1^2 + 1 - 6 = -4

f(3) = 3^2 + 3 - 6 = 9

Next, we calculate the difference in function values:

Δf = 9 - (-4) = 13

Finally, we calculate the difference in x values:

Δx = 3 - 1 = 2

Now, we can find the average rate of change:

Average rate of change = Δf/Δx = 13/2 = 6.5

Therefore, the average rate of change of f(x) between x = 1 and x = 3 is 6.5.

Answer 2

10

Step-by-step explanation:

Substitute 1 in place of x and the result is -4.

Again substitute 3 in place of x and the result is 6.

Change=6-(-4)=10