1.4 Section Exercises
For each function graphed, estimate the local maximums, local minimums and inflection points. Then specify the intervals on which the function is increasing, decreasing, concave up and concave down.
1. |
2. |
3. |
4. |
For each table below, select whether the table represents a function that is increasing or decreasing, and whether the function is concave up or concave down.
5.
| x | f(x) |
| 1 | 2 |
| 2 | 4 |
| 3 | 8 |
| 4 | 16 |
| 5 | 32 |
6.
| x | g(x) |
| 1 | 90 |
| 2 | 80 |
| 3 | 75 |
| 4 | 72 |
| 5 | 70 |
7.
| x | h(x) |
| 1 | 300 |
| 2 | 290 |
| 3 | 270 |
| 4 | 240 |
| 5 | 200 |
8.
| x | k(x) |
| 1 | 0 |
| 2 | 15 |
| 3 | 25 |
| 4 | 32 |
| 5 | 35 |
9.
| x | f(x) |
| 1 | -10 |
| 2 | -25 |
| 3 | -37 |
| 4 | -47 |
| 5 | -54 |
10.
| x | g(x) |
| 1 | -200 |
| 2 | -190 |
| 3 | -160 |
| 4 | -100 |
| 5 | 0 |
11.
| x | h(x) |
| 1 | -100 |
| 2 | -50 |
| 3 | -25 |
| 4 | -10 |
| 5 | 0 |
12.
| x | k(x) |
| 1 | -50 |
| 2 | -100 |
| 3 | -200 |
| 4 | -400 |
| 5 | -900 |
Use a graph to estimate the local extrema and inflection points of each function, and to estimate the intervals on which the function is increasing, decreasing, concave up, and concave down.
- [latex]f(x)={{x}^{4}}-4{{x}^{3}}+5[/latex]
- [latex]h(x)={{x}^{5}}+5{{x}^{4}}+10{{x}^{3}}+10{{x}^{2}}-1[/latex]
- [latex]g(t)=t\sqrt{t+3}[/latex]
- [latex]k(t)=3{{t}^{2/3}}-t[/latex]
- [latex]m(x)={{x}^{4}}+2{{x}^{3}}-12{{x}^{2}}-10x+4[/latex]
- [latex]n(x)={{x}^{4}}-8{{x}^{3}}+18{{x}^{2}}-6x+2[/latex]
