Use a computer algebra system to find the second derivative of the function. \

$$h(x)=x \sqrt{x^2-1}$$

A newspaper headline stated that at a recent budget workshop, nearly three dozen people supported a sales tax increase to help deal with the city's financial deficit (San Lids Obispo Tribune, January 22, 2005). This conclusion was based on data from a survey acknowledged to be unscientific, in which 34 out of the 43 people who chose to attend the budget workshop recommended raising the sales tax. Briefly discuss why the survey was described as "unscientific" and how this might limit the conclusions that can be drawn from the survey data.

Suppose that a group of 1000 orange trees is laid out in 40 rows of 25 trees each. To determine the sugar content of fruit from a sample of 30 trees, researcher A suggests randomly selecting five rows and then randomly selecting six trees from each sampled row. Researcher B suggests numbering each tree on a map of the trees from 1 to 1000 and using random numbers to select 30 of the trees. Which selection method is preferred? Explain.

A survey of affluent Americans (those with incomes of $\$ 75,000$ or more) indicated that $57 \%$ would rather have more time than more money (USA Today, Janu ary 29, 2003). a. What condition on how the data were collected would make the generalization from the sample to the population of af flu ent Americans reasonable? b. Would it be reasonable to generalize from the sample to say that $57 \%$ of all Americans would rather have more time than more money? Explain.

The article “Television’s Value to Kids: It’s All in How They Use It” (Seattle Times, July 6, 2005) described a study in which researchers analyzed standardized test results and television viewing habits of 1700 children. They found that children who averaged more than 2 hours of television viewing per day when they were younger than 3 tended to score lower on measures of reading ability and short-term memory. a. Is the study described an observational study or an experiment? b. Is it reasonable to conclude that watching two or more hours of television is the cause of lower reading scores? Explain.

For each of the following situations, give a set of possible data values that might arise from making the observations described. a. The manufacturer for each of the next 10 automobiles to pass through a given intersection is noted. b. The grade point average for each of the 15 seniors in a statistics class is determined. c. The number of gas pumps in use at each of 20 gas stations at a particular time is determined. d. The actual net weight of each of 12 bags of fertilizer having a labeled weight of 50 pounds is determined. e. Fifteen different radio stations are monitored during a 1-hour period, and the amount of time devoted to commercials is determined for each.

Use a computer algebra system to find the second derivative of the function. \

$$g(\theta)=\tan 3 \theta-\sin (\theta-1)$$

Use the utility to graph the function and its tangent line in the same viewing window. \

$$y=\left(t^2-9\right) \sqrt{t+2}, \quad(2,-10)$$

Find an equation of the tangent line to the graph of the function at the given point \

$$y=\left(t^2-9\right) \sqrt{t+2}, \quad(2,-10)$$

Use a graphing utility to find the derivative of the function at the given point \

$$y=\left(t^2-9\right) \sqrt{t+2}, \quad(2,-10)$$

Use a computer algebra system to find the second derivative of the function.
$g(x)=\dfrac{6 x-5}{x^2+1}$

Find the derivative by the limit process. \

$$f(x)=3$$

Consider the linear function $y=a x+b$. If $x$ changes at a constant rate, does $y$ change at a constant rate? If so, does it change at the same rate as $x$ ? Explain.

Find the derivative of the function. \

$$f(x)=\left(9-x^2\right)^{2 / 3}$$