Section Exercises
1. Can the average rate of change of a function be constant? 2. If a function [latex]f[/latex] is increasing on [latex]\left(a,b\right)[/latex] and decreasing on [latex]\left(b,c\right)[/latex], then what can be said about the local extremum of [latex]f[/latex] on [latex]\left(a,c\right)?[/latex] 3. How are the absolute maximum and minimum similar to and different from the local extrema? 4. How does the graph of the absolute value function compare to the graph of the quadratic function, [latex]y={x}^{2}[/latex], in terms of increasing and decreasing intervals? For exercises 5–15, find the average rate of change of each function on the interval specified for real numbers [latex]b[/latex] or [latex]h[/latex]. 5. [latex]f\left(x\right)=4{x}^{2}-7[/latex] on [latex]\left[1,\text{ }b\right][/latex] 6. [latex]g\left(x\right)=2{x}^{2}-9[/latex] on [latex]\left[4,\text{ }b\right][/latex] 7. [latex]p\left(x\right)=3x+4[/latex] on [latex]\left[2,\text{ }2+h\right][/latex] 8. [latex]k\left(x\right)=4x - 2[/latex] on [latex]\left[3,\text{ }3+h\right][/latex] 9. [latex]f\left(x\right)=2{x}^{2}+1[/latex] on [latex]\left[x,x+h\right][/latex] 10. [latex]g\left(x\right)=3{x}^{2}-2[/latex] on [latex]\left[x,x+h\right][/latex] 11. [latex]a\left(t\right)=\frac{1}{t+4}[/latex] on [latex]\left[9,9+h\right][/latex] 12. [latex]b\left(x\right)=\frac{1}{x+3}[/latex] on [latex]\left[1,1+h\right][/latex] 13. [latex]j\left(x\right)=3{x}^{3}[/latex] on [latex]\left[1,1+h\right][/latex] 14. [latex]r\left(t\right)=4{t}^{3}[/latex] on [latex]\left[2,2+h\right][/latex] 15. [latex]\frac{f\left(x+h\right)-f\left(x\right)}{h}[/latex] given [latex]f\left(x\right)=2{x}^{2}-3x[/latex] on [latex]\left[x,x+h\right][/latex] For exercises 16–17, consider the graph of [latex]f[/latex].






Year | Sales (millions of dollars) |
1998 | 201 |
1999 | 219 |
2000 | 233 |
2001 | 243 |
2002 | 249 |
2003 | 251 |
2004 | 249 |
2005 | 243 |
2006 | 233 |
Year | Population (thousands) |
2000 | 87 |
2001 | 84 |
2002 | 83 |
2003 | 80 |
2004 | 77 |
2005 | 76 |
2006 | 78 |
2007 | 81 |
2008 | 85 |

