Question

Find the average rate of change of f ( x ) = -2x^2 + 4x + 2 as X varies from 1.2 to 3.8

Answer 1

Here we need to find the average rate of change of
`f(x)`.

Now,

`f(x)=-2x^2+4x+2`

Let us find out the value of
`f(x)` at the point
`x=1.2`.

Plugging
`x=1.2` in the equation we get:

`f(1.2)=-2(1.2)^2+4(1.2)+2=-2* 1.44+4.8+2=-2.88+4.8+2=3.92`

So,

`f(1.2)=3.92`

Now calculating the value of
`f(x)` at
`x=3.8`.

`f(3.8)=-2(3.8)^2+4(3.8)+2=-2(14.44)+15.2+2=-28.88+15.2+2=-11.68`

So,

`f(3.8)=-11.68`

Now that we have the values of the function at two distinct points, we can find the average by using the formula given below:

`Avg= (sum)/(n)`, where 'n' represents the number of values and that is two in our case and sum represents the sum of the values of the function.

Therefore,

`Avg= (3.92+(-11.68))/(2) =(-7.76)/(2) =-3.88`

So, the average rate of change of the function
`f(x)` from 1.2 to 3.8 is
`-3.88`.