Rolle's Theorem and The Mean Value Theorem in Calculus
3.2
Rolle’s Theorem &
The Mean Value Theorem
p. 220
Rolle’s Theorem
•
If
f
is
continuous
on [a,b] and
differentiable
on (a, b) and
f
(a)=
f
(b), then there is at least
one number,
c
, such that
*could be more than one place
Mean Value Theorem
•
If
f
is
continuous
on [a,b] and
differentiable
on
(a,b) then there exists a number,
c
, such that:
*says the average rate of change
must = instantaneous rate of change at some
time on [a,b].
Picture
Homework
p. 224
9-21 EO odd, 25, 37-49 odd,
53, 55, 81-83 all
Rolle's Theorem states that for a continuous and differentiable function on a closed interval with equal function values at the endpoints, there exists at least one point where the derivative is zero. The Mean Value Theorem asserts that for a continuous and differentiable function on an interval, there exists a point where the average rate of change equals the instantaneous rate of change.
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Presentation Transcript
3.2 Rolle s Theorem & The Mean Value Theorem p. 220
Rolles Theorem If f is continuous on [a,b] and differentiable on (a, b) and f(a)=f(b), then there is at least one number, c, such that *could be more than one place
Mean Value Theorem If f is continuous on [a,b] and differentiable on (a,b) then there exists a number, c, such that: *says the average rate of change must = instantaneous rate of change at some time on [a,b].
Homework p. 224 9-21 EO odd, 25, 37-49 odd, 53, 55, 81-83 all
