Posted by **Sandy** on Monday, February 7, 2011 at 1:59pm.

Determine whether Rolle's Theorem is valid

f(x) = 3 - |x - 2| for [-1, 5]

if so, find c.

if not, tell why.

- AP Calculus -
**MathMate**, Monday, February 7, 2011 at 6:34pm
Rolle's theorem states that:

"Suppose that y=f(x) is continuous at every point of the closed interval [a,b] and *differentiable* at every point of its interior (a,b). If

f(a)=f(b),

then there is at least one number c in (a,b) at which f'(c)=0.

Here all conditions are satisfied except one. It is not differentiable at x=2, so Rolle's theorem does not apply. Differentiable means that f'(x) exists, but f'(2) is an interior point of (-1,5) and f'(2) does not exist. Check the graph below. Post if more help is required.

http://img28.imageshack.us/img28/9139/1297105145.png

## Answer this Question

## Related Questions

- Calculus - Determine whether Rolle's Theorem can be applied to f on the closed ...
- Math - Determine whether Rolle's Theorem can be applied to f on the closed ...
- Calculus - 1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the ...
- calc - Verify that the function satisfies the three hypotheses of Rolle's ...
- calc - Verify that the function satisfies the three hypotheses of Rolle's ...
- Calculus - Determine if Rolle's Theorem applies to the given function f(x)=2 cos...
- URGENT!! PLEASE Calc - Verify that the function satisfies the three hypotheses ...
- Calculus - Use the graph of f(x)=x^2/(x^2-4) to determine on which of the ...
- calculus - Referring to the Mean Value Theorem and Rolle's Theorem, how can I ...
- calculus - Show that the function f(x)=4x^3−15x^2+9x+8 satisfies the ...