Question

Question 3

If y=x2+3x, then the average rate of change of y with respect to x over the closed interval 1

Answer 1

`Rate = 19`

Explanation:

Given

`y = x^2 + 3x`

`1 \le x \le 15`

Required

Determine the average rate of change

This is calculated as:

`Rate = (f(b) - f(a))/(b - a)`

Where

a = 1 and b = 15

So, we have:

`Rate = (f(15) - f(1))/(15 - 1)`

`Rate = (f(15) - f(1))/(14)`

Solve f(15):

`f(15) = 15^2 + 3*15 = 270`

Solve f(1)

`f(1) = 1^2 + 3*1 = 4`

So:

`Rate = (f(15) - f(1))/(14)`

`Rate = (270- 4)/(14)`

`Rate = (266)/(14)`

`Rate = 19`