Algebra Equations Worksheets With Answer Keys Page 6
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20Chapter 5
6
( ) =
x
−
3. Let
f x
e
x .
(a) At what x-values does f have relative extrema?
( )
( )
′
′
x
=
x
−
=
−
+1
f
x
e
1
f
x
e
1
=
+1
x
0
=
x
−
0
e
1
+1 Justify extrema
x
=
e
1
=
x
0
( )
( )
′ −
′
<
>
=
Since
f
1
0
and
f
1
0
, a relative minimum occurs at
x
0
.
1
( )
∫
′ f
(b) Which expression has the least value:
f x dx or
( )
1
? Justify
−
1
your answer.
( )
′ f
1
+1
1
1
∫
= −
≈
f x dx
( )
e
2.350
e
+2 Supporting work
−
1
( )
′
= − ≈
f
1
e
1 1.718
( )
′ f
has the least value.
1
a
a
⎛
⎞
2
a
∫
( )
∫
′
=
=
a
−
−
(c) Given
f x dx
( )
f a , find a .
+1
f x dx
( )
e
1
⎜
⎟
2
⎝
⎠
0
0
( )
′
=
a
−
+ 1
f a
e
1
( )
′
a
a
=
a
−
a
f a
e
1
=
+1
a
0
∫
∫
∫
( )
x
′
=
−
=
f x dx
( )
e
x dx
f x dx
( )
f a
0
0
0
a
2
a
2
x
a
−
− =
a
−
e
1
e
1
x
=
−
e
2
2
0
2
a
⎛
⎞
−
=
2
0
a
=
a
−
−
e
1
2
⎜
⎟
2
⎝
⎠
=
a
0
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