List three ways of writing the first partial derivative with respect to x of $z=f(x, y)$.

An oil company wishes to construct a pipeline from its offshore facility A to its refinery B. The offshore facility is 2 miles from shore, and the refinery is 1 mile inland. Furthermore, A and B are 5 miles apart.

The cost of building the pipeline is $\3 million per mile in the water and$4 million per mile on land. So, the cost of the pipeline depends on the location of point P, where it meets the shore. What would be the most economical route of the pipeline?

Imagine that you are to write a report to the oil company about this problem. Let x be the distance shown in the figure. Determine the cost of building the pipeline from A to P and the cost of building it from P to B. Analyze some sample pipeline routes and their corresponding costs. For instance, what is the cost of the most direct route? Then use calculus to determine the route of the pipeline that minimizes the cost. Explain all steps of your development and include any relevant graphs.

Use a graphing utility to graph $z=x^3-3 x y+y^3$ using the bounds $0 \leq x \leq 3$, $0 \leq y \leq 3$, and $-3 \leq z \leq 3$. This view makes it appear as though the surface has an absolute minimum. Does the surface have an absolute minimum? Why or why not?

In each of the three figures below, the cue ball is about to strike a stationary ball at point $P$. Explain how you can use the normal line to the stationary ball at point $P$ to describe the resulting motion of each of the two balls. Assuming that each cue ball has the same speed, which stationary ball will acquire the greatest speed? Which will acquire the least? Explain your reasoning.

For a function f(x, y), when does the directional derivative at the point ($x_{0}$, $y_{0}$) equal the partial derivative with respect to x at the point ($x_{0}$, $y_{0}$)? What does this mean graphically?

Consider w=f(x, y), where x=g(s, t) and y=h(s, t). Describe two ways of finding the partial derivatives $\partial w /\partial s$ and $\partial w / \partial t$.

For a function of two variables, describe (a) relative minimum, (b) relative maximum, (c) critical point, and (d) saddle point.

Evaluate the function at the given values of the independent variables. Simplify the results. $f(x, y)=x^{2} y-3$ (a) f(0, 4), (b) f(2, -1), (c) f(-3, 2), (d) f(x, 7).

Describe the change in accuracy of dz as an approximation of $\Delta z$ as $\Delta x$ and $\Delta y$ increase.

How are quadric surfaces and conic sections related?

Drugs that increase heart rate, blood pressure, and breathing rate are a. stimulants b. depressants. c. opiates. d. barbiturates.

Which of the following is NOT an endocrine gland? (A) thyroid gland (B) pituitary gland (C) parathyroid gland (D) sweat gland (E) adrenal gland

Write the correct word in the space next to given definition.
______________ a social class of rank, wealth, or profession

The desire to maximize profits can work against racial and other types of discrimination. To see this, consider two equally productive accountants named Ted and Jared. Ted is black, and Jared is white. Both can complete 10 audits per month.

a. Suppose that for any accounting firm that hires either Ted or Jared, all the other costs of performing an audit (going rate that must be paid to hire an accountant is $7,000 per month, how much will it cost an accounting firm to produce one audit if it hires either Ted orJared to do the work.

b. If the market price that accounting firms charge their clients for an audit is$1,800, what would the accounting profit per audit be for a firm that hired either Ted or Jared? What is the profit rate as a percentage?

c. Suppose that firm A dislikes hiring black accountants, while firm B is happy to hire them. So Ted ends up working at firm B rather than firm A. If Ted works 11 months per year, how many audits will he complete for firm B each year? How much in accounting profits will firm B earn each year from those audits?

d. Because firm A passed on hiring Ted because he was black, firm A is forgoing the profits it could have earned if it had hired Ted. If the firm is willing to forgo up to $5,000 per year in profit to avoid hiring blacks, by how many dollars will firm A regret its decision not to hire Ted?