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Differentiation
topics
Difference quotient
for f at x = a
If f is differentiable at x = a…
Then f is continuous
at x = a
At some point in the
interval the
instantaneous rate of
change equals the
average rate of change
If f is differentiable at x = a…
The graph of f
has a vertical
tangent
Critical points
of f
•At the endpoints of the
domain
•Where f’ does not exist
•Where f’ = 0
f has a maximum at x = a
nd derivative test)
(2
f has a minimum at x = a
nd derivative test)
(2
What is a point
of inflection?
A point where the
graph of f changes
concavity
Velocity
Speed
Acceleration
(in terms of velocity)
Acceleration
(in terms of position)
Increasing
Speed
Velocity and
acceleration have
the same sign
Decreasing
Speed
Velocity and
acceleration have
opposite signs
An object is at
rest when…
Differentiation topics
Differentiation topics

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Differentiation topics