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Rolle's Theorem

​
f(x) =
-
2
x
+2x+3
y value
1
solutions
find
show
c
0
​Rolle's theorem states that if a function
f
is continuous on
[a,b]
and differentiable on
(a,b)
with
f(a)=f(b)
, then there is at least one
x
value
c
with
a<c<b
where the derivative is 0. In terms of the graph, this means that the function has a horizontal tangent line at some point
c
in the interval.
Rolle's theorem can be thought of as a lemma or a corollary of the mean value theorem in calculus.
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