Question

Find the average rate of change of f(x)=x^3 over the interval -1 to 3.

Answer options are:
3
5
7
9

Answer 1

f(x) = x^3

The interval is -1 to 3

The intervals here are X

So we just plug in the x values with these 2 numbers.

F(x) is basically “y”

Y= x^3

For -1

y= (-1)^3

Y= -1

For 3

Y= 3^3

Y= 27

So now we have the y values we can’t forget the x values originally used to plug it in.

So for -1, the x value is -1 and y is -1, therefore

(-1,-1)

For 3, the x value is 3 and the y value is 27, therefore

(3,27)

Find the rate of change which is basically the slope, you do this by

(y2- y1)/(x2 - x1)

*1 and 2 are just subscripts*

It doesn’t matter for ay order so lets just do

-1 - 27 / -1 - 3

= -28 / -4

= 7

The answer is 7