함수와 그래프 전체 문제

For the following exercises, consider the graph in (the referenced figure).

If the complete graph of the function is shown, estimate the absolute maximum and absolute minimum.

(the referenced table) gives the annual sales (in millions of dollars) of a product from 1998 to 2006. What was the average rate of change of annual sales (a) between 2001 and 2002, and (b) between 2001 and 2004?

(the referenced table) gives the population of a town (in thousands) from 2000 to 2008. What was the average rate of change of population (a) between 2002 and 2004, and (b) between 2002 and 2006?

For the following exercises, find the average rate of change of each function on the interval specified.

$f(x)={x}^{2}$ on $[1,\,5]$

For the following exercises, find the average rate of change of each function on the interval specified.

$h(x)=5-2{x}^{2}$ on $[-2,4]$

For the following exercises, find the average rate of change of each function on the interval specified.

$q(x)={x}^{3}$ on $[-4,2]$

For the following exercises, find the average rate of change of each function on the interval specified.

$g(x)=3{x}^{3}-1$ on $[-3,3]$

For the following exercises, find the average rate of change of each function on the interval specified.

$y=\frac{1}{x}$ on $[1,\,3]$

For the following exercises, find the average rate of change of each function on the interval specified.

$p(t)=\frac{({t}^{2}-4)(t+1)}{{t}^{2}+3}$ on $[-3,1]$

For the following exercises, find the average rate of change of each function on the interval specified.

$k(t)=6{t}^{2}+\frac{4}{{t}^{3}}$ on $[-1,3]$

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.

$f(x)={x}^{4}-4{x}^{3}+5$

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.

$h(x)={x}^{5}+5{x}^{4}+10{x}^{3}+10{x}^{2}-1$

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.

$g(t)=t\sqrt{t+3}$

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.

$k(t)=3{t}^{\frac{2}{3}}-t$

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.

$m(x)={x}^{4}+2{x}^{3}-12{x}^{2}-10x+4$

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing.

$n(x)={x}^{4}-8{x}^{3}+18{x}^{2}-6x+2$

The graph of the function $f$ is shown in (the referenced figure).

Based on the calculator screen shot, the point $(1.333,\,5.185)$ is which of the following?

• ⓐa relative (local) maximum of the function
• ⓑthe vertex of the function
• ⓒthe absolute maximum of the function
• ⓓa zero of the function

Let $f(x)=\frac{1}{x}.$ Find a number $c$ such that the average rate of change of the function $f$ on the interval $(1,c)$ is $-\frac{1}{4}.$

Let $f(x)=\frac{1}{x}$ . Find the number $b$ such that the average rate of change of $f$ on the interval $(2,b)$ is $-\frac{1}{10}.$

At the start of a trip, the odometer on a car read 21,395. At the end of the trip, 13.5 hours later, the odometer read 22,125. Assume the scale on the odometer is in miles. What is the average speed the car traveled during this trip?