Concavity And The Second Derivative Test Worksheet With Answers Page 9
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9nd
Calculus Maximus
WS 3.4: Concavity & 2
Deriv Test
20. Use the Second Derivative Test (if possible) to locate and justify the local extrema of the following
functions. If the Test Fails, justify using the First Derivative Test.
( )
( )
3
2
5
3
=
−
=
−
(a)
f x
x
3
x
(b)
f x
3
x
20
x
( )
( )
−
(
)
2
x
=
=
−
(c)
f x
2
x
ln
x
(d)
f x
e
x
7
21. Coffee is being poured into Mr. Korpi’s mug (shown below) at a constant rate (measured in ounces per
second). If the cup is filled to the brim, sketch a rough graph of the depth of the coffee in the mug, in
inches, as a function of time, in seconds. Be sure to account for the shape of the graph, especially in
terms of its concavity. What is the significance of the inflection point?
6 inches
I
3 inches
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2. Family
3. Speling
0 inches
Page 9 of 9
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