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Chapter 2: More on Functions
The graph starts decreasing from the left and stops decreasing at the relative minimum. From this point it increases to the relative maximum and then decreases again. Thus the function is increasing on (0.103, 3.601) and is decreasing on (−∞, 0.103) and on (3.601, ∞). 17.
20.
y 5 4 3 2 1
y
–5 –4 –3 –2 –1
–1
5
–2
4
–3
3
–4
f (x ) = x 2
2
1
2
3
4
5
x
f (x ) = | x + 3 | — 5
–5
1 –5 –4 –3 –2 –1
–1
1
2
3
4
5
Increasing: (−3, ∞)
x
Decreasing: (−∞, −3)
–2 –3 –4
Maxima: none
–5
Minimum: −5 at x = −3
The function is increasing on (0, ∞) and decreasing on (−∞, 0). We estimate that the minimum is 0 at x = 0. There are no maxima.
21.
y 5 4 3
18.
y
2 1
5 –5 –4 –3 –2 –1
f (x ) = 4 — x 2
4 3
–2
2
–1
1
2
3
4
5
x
f (x ) = x 2 — 6x + 10
–3
1 –5 –4 –3 –2 –1
–1
–4 1
2
3
4
5
x
–5
–2
The function is decreasing on (−∞, 3) and increasing on (3, ∞). We estimate that the minimum is 1 at x = 3. There are no maxima.
–3 –4 –5
Increasing: (−∞, 0)
22.
Decreasing: (0, ∞)
y
f (x ) =
Maximum: 4 at x = 0
10 2 — x — 8x 8
—9
6 4
Minima: none
2
19.
y
–10 –8 –6 –4 –2
5
2
4
6
8 10
x
–4
f (x ) = 5 — | x |
4
–2
–6
3
–8
2
–10
1 –5 –4 –3 –2 –1
–1
1
2
3
4
5
Increasing: (−∞, −4)
x
Decreasing: (−4, ∞)
–2 –3
Maximum: 7 at x = −4
–4 –5
Minima: none
The function is increasing on (−∞, 0) and decreasing on (0, ∞). We estimate that the maximum is 5 at x = 0. There are no minima.
23.
Beginning at the left side of the window, the graph first drops as we move to the right. We see that the function is Copyright
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