最終更新日：2024/08/03
(calculus) The theorem that any real-valued differentiable function that attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. In mathematical terms, if f:ℝ→ℝ is differentiable on (a,b) and f(a)=f(b) then ∃c∈(a,b):f'(c)=0.
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Rolle's theorem
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元となった辞書の項目
Rolle's theorem
name
(calculus)
The
theorem
that
any
real-valued
differentiable
function
that
attains
equal
values
at
two
distinct
points
must
have
a
point
somewhere
between
them
where
the
first
derivative
(the
slope
of
the
tangent
line
to
the
graph
of
the
function)
is
zero.
In
mathematical
terms,
if
f:ℝ→ℝ
is
differentiable
on
(a,b)
and
f(a)=f(b)
then
∃c∈(a,b):f'(c)=0.
意味（1）
(calculus)
The
theorem
that
any
real-valued
differentiable
function
that
attains
equal
values
at
two
distinct
points
must
have
a
point
somewhere
between
them
where
the
first
derivative
(the
slope
of
the
tangent
line
to
the
graph
of
the
function)
is
zero.
In
mathematical
terms,
if
f:ℝ→ℝ
is
differentiable
on
(a,b)
and
f(a)=f(b)
then
∃c∈(a,b):f'(c)=0.
