Question

How do I Determine whether Rollie's theorem can be applied to F on the closed interval (AB) F of X = -x squared

Answer 1

See Explanation

Explanation:

Your question is incomplete. I will take the complete question as:

`f(x) = -x^2`

`Interval: [-1,1]`

Required

Determine whether Rollie's theorem can be applied or not

First, find the coordinates of the endpoints on the closed interval [-1, 1]

`f(x) = -x^2`

`f(-1) = -(-1)^2 = -1` ------
`(-1,-1)`

`f(1) = -(1)^2 =-1` ----
`(1,-1)`

Find the derivative of f(x)

`f(x) = -x^2`

`f'(x) = -2x`

Calculate the slope (m) of the secant line i.e.
`(-1,-1)` and
`(1,-1)`

`m = (-1 - (-1))/(1 - (-1))`

`m = (-1 +1)/(1 +1)`

`m = (0)/(2)`

`m=0`

Set the derivative to the calculated slope:

`f'(x) = m`

`-2x = 0`

`x=0`

Plug in 0 for x in f'(0)

`f'(x) = -2x`

`f'(0) = -2 * 0`

`f'(0) = 0`

Since f'(0) is differentiable at x = 0. We can conclude that Rollie's theorem can be applied