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

Answer:

See Explanation

Step-by-step 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 $(1,-1)$

$m = \frac{-1 - (-1)}{1 - (-1)}$

$m = \frac{-1 +1}{1 +1}$

$m = \frac{0}{2}$

$m=0$

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