Question

Find the average rate of change of the function between the given values of x. y = 9+ 5x + 0.5x2 between x = 2 and x = 4.

Answer 1

The average rate of change is 8.

Explanation:

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Answer 2

The average rate of change is 8.

Explanation:

The formula to calculate the average rate of change of a function F(x) is:

`(F(b)-F(a))/(b-a)`

In this case, F(x) =
`0.5x^(2) +5x+9`

a=2 and b=4

You have to evaluate x=2 (which is a in the formula) and x=4 (which is b in the formula) in the function.

In order to obtain F(b) and F(a) you have to replace x=4 and x=2 in the given function:

F(b) =
`(0.5)4^(2) + 5(4) +9= 37`

F(a) =
`(0.5)2^(2) + 5(2)+9=21`

`(F(b)-F(a))/(b-a) = (37-21)/(4-2)=(16)/(2) = 8`

The answer is 8.