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210 Chapter 3 Exponential and Logarithmic Functions
83.
hx 4x ln x 84.
(a)
6
fx
(a)
x
ln x
4
−6
6
−2
10
−2
(b) Domain: 0,
(c) Increasing on 0.368,
Decreasing on 0, 0.368
(d) Relative minimum: 0.368, 1.472
−4
(b) Domain: 0, 1 1,
(c) Increasing on 2.72,
Decreasing on 0, 1 1, 2.72
(d) Relative minimum: 2.72, 2.72
85.
fx ln
x 2
x 1 86.
fx ln
2x
x 2
(a)
4
(a)
4
−6 6
−6 6
−4
−4
(b)
x 2
Critical numbers: 1, 2
x 1 > 0;
Test intervals: , 2, 2, 1, 1,
Testing these three intervals, we see that the
domain is , 2 1, .
(c) The graph is decreasing on , 2 and
decreasing on 1, .
(d) There are no relative maximum or
minimum values.
(b)
2x
Critical numbers: 0, 2
x 2 > 0;
Test intervals: , 2, 2, 0, 0,
Testing these three intervals, we see that the
domain is , 2 0, .
(c) The graph is increasing on , 2 and
increasing on 0, .
(d) There are no relative maximum or
minimum values.
87.
fx ln
x 2
10 88.
(a)
(b)
2
−6 6
−6
x 2
10 > 0 ⇒ x 0;
Domain: all x 0
(c) The graph is increasing on 0, and
decreasing on , 0.
(d) There are no relative maximum or
relative minimum values.
fx ln
x
x 2 1
(a)
0
−1 5
−4
(b) Domain: x > 0
(c) The graph is increasing on 0, 1 and
decreasing on 1, .
(d) Relative maximum: 1, 0.693
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