Consider the function f(x)=x^2−4x+5 on the interval [0,4]. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval.
f(x) is on [0,4];
f(x) is on (0,4);
and f(0)=f(4)= .

Then by Rolle's theorem, there exists a c such that f′(c)=0.
Find the value c.
c=

Question

Consider the function f(x)=x^2−4x+5 on the interval [0,4]. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval. 
f(x) is  on [0,4]; 
f(x) is  on (0,4); 
and f(0)=f(4)= . 

Then by Rolle's theorem, there exists a c such that f′(c)=0.
Find the value c. 
c=

anonymous · Answer

when you get the answer not that it is right smack in the middle of the interval
always is if your function is a quadratic

anonymous · Answer

This is a parabola and is symmetric about a line passing through its vertex.
Find the vertex.

anonymous · Answer

$f(0)=5$ and $f(4)=5$  as well and since $f(0)=f(4)$ you can use can use lou rawl's theorem and find where the derivative is 0 
as @CliffSedge  said, that is the first coordinate of the vertex  
or take the derivative, set it equal to zero and solve, and you will get the first coordinate of the vertex that way too

anonymous · Answer

And by symmetry, the vertex is halfway between two equal function values.

anonymous · Answer

Kinda like what you first said, above.

anonymous · Answer

and...
when you next see the mean value theorem, if you have a quadratic, the number that satisfies the theorem will always be in the center of the interval, just like it is in this case

anonymous · Answer

^ good point.

anonymous · Answer

well i got everything except the last part 
Then by Rolle's theorem, there exists a c such that f′(c)=0.
Find the value c. 
c=