# Thread: One Quick Mean Value Problem!!!

1. ## One Quick Mean Value Problem!!!

1. Consider the function on the interval . Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval.
is ???? on ;
is ???? on ;
and ?????.

2. Please someone help me?? or explain/ give hints!!!

3. 1 it is differentiable on the open interval

2 it is continuous on the closed interval

3 f(0)=f(4)=5

SEE...
http://en.wikipedia.org/wiki/Rolle's_theorem

If a real-valued function ƒ is continuous on a closed interval [a,b], differentiable on the open interval (a, b),
and ƒ(a) = ƒ(b), then there is some real number c in the open interval (a, b) such that $f'(c)=0$.

So set 2x-4=0 and solve for x.

4. Thanks matheagle.

Originally Posted by matheagle
1 it is differentiable on the open interval

2 it is continuous on the closed interval

3 f(0)=f(4)=5

SEE...
http://en.wikipedia.org/wiki/Rolle's_theorem

If a real-valued function ƒ is continuous on a closed interval [a,b], differentiable on the open interval (a, b),
and ƒ(a) = ƒ(b), then there is some real number c in the open interval (a, b) such that $f'(c)=0$.

So set 2x-4=0 and solve for x.