Extrema On An Interval Worksheet With Answers- Calculus Maximus Ws 3.1
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7Calculus Maximus
WS 3.1: Extrema on an Interval
Name_________________________________________ Date________________________ Period______
Worksheet 3.1—Extrema on an Interval
Show all work. No calculator, except on problem #6.
Short Answer
[
]
( )
2/3
−
=
−
1. Let f be the functioned defined on
1, 2
by
f x
3
x
2
x
.
( )
(a) Find the domain of
f x .
( )
( )
′
′
(b) Find
f x
and the domain of
f x
.
( )
(c) Determine if the EVT applies to
f x on the given interval. If it does, find the max and min values
guaranteed by the theorem. Justify using the Closed Interval Argument. Show the work that leads to
your answer.
[ ]
x = , an
2. Sketch the graph of a function f that is continuous on
1,5 and has an absolute minimum at
1
x = , a local maximum at
x = , and a local minimum at
x = . Answers will
absolute maximum at
5
2
4
vary.
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