Question

Calculate the average rate of change of y=x2+3x−2 on the interval 1≤x≤2

Answer 1

The rate of change for the given function is 6.

Explanation:

Given function is:

`y = x^2+3x-2`

The interval on which we have to find the rate of change is:

1≤x≤2

Here

a = 1

b = 2

We have to find the values of function on both points

Putting 1 in place of input (x)

`y_a= (1)^2+3(1)-2\\= 1+3-2\\=2`

Putting x = 2

`y_b = (2)^2+3(2)-2\\= 4+6-2\\=8`

The rate of change is calculated by using the following formula

`Rate\ of\ change = (y_b-y_a)/(b-a)\\=(8-2)/(2-1)\\= (6)/(1)\\=6`

Hence,

The rate of change for the given function is 6.