Question

Find the average rate of change of f(x)=2x^2-7x from x=2 to x=6

Answer 1

Explanation:

The average rate of change of a function f between a and b (a< b) is :

R =[f(b)-f(a)] ÷ (a-b)

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Let R be the average rate of change of this function

f(6) = 2×6^2 - 7×6 = 72-42 = 30

f(2) = 2×2^2 - 7×2 = 8-14 = -6

R = [f(6) - f(2)]÷ (6-2)

R = [30-(-6)] ÷ 4

R = -36/4

R = -9

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The average rate of change of this function is -9

Answer 2

`(\Delta y)/(\Delta x) =9`

Explanation:

You can find the average rate of change of any function using the following formula:

`Average\hspace{3} rate\hspace{3} of \hspace{3} change=(\Delta y)/(\Delta x) =(f(x_2)-f(x_1))/(x_2-x_1)`

Now, let:

`x_1=2\\\\and\\\\x_2=6`

Let's evaluate the function for
`x_1` and
`x_2` :

`f(x_1)=2(2)^(2) -7(2)=2*4-7*2=8-14=-6\\\\f(x_2)=2(6)^(2) -7(6)=2*36-7*6=72-42=30`

Therefore, the average rate of change of the function over the interval given is:

`(\Delta y)/(\Delta x) =(f(6)-f(2))/(6-2) =(30-(-6))/(6-2) =9`