Calculus 12
AP
Unit III Assignments
Chapter 4 – Applications of the Derivative
Feb 20
Wed
•
4.1
Extreme Value of Functions
•
Absolute / Relative Extreme Values
•
Critical Point 
′
f
=
0 or
′
f
undefined
•
Use graphs of the function
y
=
f x
( )
to help with analysis
Assignment III1
Page 184 – 185 #1 – 14 all, 17, 19*, 23*, 25*, 29* (for * questions just use your
Adjusted
calculator – not calculus) . 35ab, 37, 39, 41, 45 – 49 all
Feb 21
Thurs
•
4.2 Mean Value Theorem
•
′
f
c
( )=
f b
( )
f a
( )
b

a
•
Increasing and decreasing functions
•
′
f
>
0
⇒
f
is increasing;
′
f
<
0
⇒
f
is increasing
Assignment III–2
Page 192 – 193 #1 – 23 odd, 35 – 42 all
Feb 22
Fri
•
4.3
Connecting
′
f
and
′
′
f
with the Graph of
f
•
First Derivative Test for Local Extrema (Thumbnail Sketch)
•
Concavity;
′
′
f
>
0
⇒
f
is concave up;
′
′
f
<
0
⇒
f
is concave down
•
Inflection point – where concavity changes;
′
′
f
=
0
⇒
f
has possible
inflection point
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 Spring '10
 John
 Calculus, Critical Point, Derivative, 1966, 1971, 1947

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