Question

Consider the function f ( x ) = 1 − 4 x 2 on the interval [ − 1 , 3 ] . Find the average or mean slope of the function on this interval, i.e. f ( 3 ) − f ( − 1 ) 3 − ( − 1 ) =

Answer 1

The average slope is 8.

Explanation:

Let f be defined on the closed interval [a, b]. The average slope of f between a and b is the quotient

average slope =
`(f(b)-f(a))/(b-a)`

To find the average slope of the function
`f(x)=1-4x^2` on the interval [-1, 3] you have to evaluate your function in the interval and then divide by the interval.

So,

`f(-1)=1-4(-1)^2=-3\\\\f(3)=1-4(3)^2=-35`

The average slope is
`(f(3)-f(-1))/(3+1)= (-3+35)/(3+1)=(32)/(4)=8`