Algebra Equations Worksheets With Answer Keys Page 14
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20Chapter 5
14
( )
( )
( )
=
2
=
2
7. Let
f x
( ) arccos
x
and
g x
arcsin
x
.
(a) At what x- values does f have relative extrema?
(
)
−
−
2
x
′ −
2
x
>
f
0.5
0
( )
( )
′
′
=
=
f
x
+1
f
x
( )
−
4
−
4
1
x
1
x
′
=
f
0
0
=
+1
x
0
−
2
x
( )
′
<
f
0.5
0
=
0
+1 Justify extrema
−
4
1
x
A relative maximum occurs
=
x
0
x = .
at
0
(b) Use technology to determine the area of the region bounded
by f and g .
x ≈ ±
Using technology, we determine points of intersection at
+1
0.841
x ≈ ±
0.841
.
0.841
(
)
( )
∫
2
−
2
+1
arccos( ) arcsin
x
x
dx
0.841
(
)
( )
∫
2
−
2
≈
arccos( ) arcsin
x
x
dx
1.815
−
0.841
+1 1.815
−
0.841
( )
( )
( )
( )
′
′
′
′
=
−
=
−
(c) Define ( )
h x
f x
( )
g x
( )
. Write
h x
in terms of
+1
h x
f
x
g x
( )
( )
( )
′
′
′
= −
f
x
.
+ 1
g x
f
x
( )
( )
′
′
=
+1
h x
2
f
x
( )
( )
( )
′
′
′
=
−
h x
f
x
g x
(
)
( )
( )
′
′
=
− −
f
x
f
x
( )
′
=
2
f
x
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