Question

Consider the function h(x) = 7x^2 + 17x - 5

A) What is the average rate of change of h from 9 to 16?

B) What is the average rate of change of h from 4 to 12

Answer 1

A) 192

B) 129

Explanation:

Given function :

`\sf h(x) = 7x^2 + 17x - 5`

In order to find the average rate of change of the function h(x) from one point to another, we can use the formula:

`\textsf{Average Rate of Change }\sf =( (h(b) - h(a)) )/((b - a))`

Where:

• "a" and "b" are the x-values representing the two points.
• h(a) and h(b) are the corresponding function values.

A) Average Rate of Change of h from 9 to 16:

- a = 9

- b = 16

First, calculate h(9) and h(16):

`\sf h(9) = 7(9)^2 + 17(9) - 5 = 567 + 153 - 5 = 715`

`\sf h(16) = 7(16)^2 + 17(16) - 5 = 1792 + 272 - 5 = 2059`

Now, calculate the average rate of change:

`\begin{aligned}\textsf{Average Rate of Change }&\sf = (h(16) - h(9))/(16 - 9) \\\\ &\sf = (2059 - 715)/( 7) \\\\ &\sf = (1344)/(7)\\\\ &\sf = 192 \end{aligned}`

Therefore,

The average rate of change of h from 9 to 16 is 192.

Similarly:

B) Average Rate of Change of h from 4 to 12:

- a = 4

- b = 12

First, calculate h(4) and h(12):

`\sf h(4) = 7(4)^2 + 17(4) - 5 = 112 + 68 - 5 = 175`

`\sf h(12) = 7(12)^2 + 17(12) - 5 = 1008 + 204 - 5 = 1207`

Now, calculate the average rate of change:

`\begin{aligned}\textsf{Average Rate of Change }&\sf = (h(12) - h(4))/(12 - 4) \\\\ &\sf = (1207 - 175)/( 8) \\\\ &\sf = (1032)/(8)\\\\ &\sf = 129 \end{aligned}`

Therefore,

The average rate of change of h from 9 to 16 is 129.