In Exercises I through $22$, find the critical points of the given fianctions and classify each as a relative maximum, a relative minimum, or a saddle point. (Note: The algebra in Exercises $19$ through $22$ is challenging.)

$$f(x, y)=x^3-4 x y+y^3$$

Use algebra tiles to rewrite each relation in the form $y = a ( x - h ) ^ { 2 } + k$ by completing the square.

$$\begin{array} { l } a) { y = x ^ { 2 } + 2 x + 5 } \\ b) { y = x ^ { 2 } + 4 x + 7 } \\ c) { y = x ^ { 2 } + 6 x + 3 } \end{array}$$

Underline the correct pronoun. Identify the case by writing nom. (nominative) or obj. (objective) in the blank. Some sentences have more than one pronoun to identify./ _____These algebra problems confuse Rashonda as much as (I, me)

Extend the class linkedListType by adding the following operations:

1. Find and delete the node with the smallest info in the list. (Delete only the first occurrence and traverse the list only once.)

2. Find and delete all occurrences of a given info from the list. (Traverse the list only once.)

Add these as abstract functions in the class linkedListType and provide the definitions of these functions in the class unorderedLinkedList. Also, write a program to test these functions.

Match the following types of theory with the appropriate description.

1. Middle-range theory
2. Shared theory
3. Grand theory
4. Practice theory

a. Very abstract; attempts to describe nursing in a global context

b. Specific to a particular situation; brings theory to the bedside

c. Applies theory from other disciplines to nursing practice

d. Addresses a specific phenomenon and reflects practice

Suppose we want to extend the PositionalList abstract data type with a method, moveToFront(p), that moves the element at position p to the front of a list (if not already there), while keeping the relative order of the remaining elements unchanged. Show how to implement this method using only existing methods of the PositionalList interface (not details of our LinkedPositionalList implementation).

Then, redo the problem, but by providing an implementation within the class LinkedPositionalList that does not create or destroy any nodes.

Underline each simple subject once and each simple predicate twice. Label each preposition $prep$., each direct object $d.o$., and each indirect object $i.o$.
Ms. Watkins asked Jenny an algebra question.

In each of the following problems, a. Write the form for the particular solution $y_{p}(x)$ for the method of undetermined coefficients. b. Use a computer algebra system to find a particular solution to the given equation. $y^{\prime \prime}-y^{\prime}-2 y=x^{2} e^{x} \sin x$

A symbol is an object, person, or idea that represents something else, usually an abstract concept. For example, on the literal level, a flag is a piece of cloth. However, a flag can also be the symbol of a nation. In this story, several objects are used as symbols. Write a brief description of what the following items symbolized in this story.

the contents of the dead man's pocket, as envisioned by Tom in a police report about his death

Slope Fields Use a computer algebra system to graph the slope field for the differential equation and graph the solution satisfying the specified initial condition.

$$\frac{dy}{dx}=\frac{2y}{\sqrt{16-x^2}},\ y(0)=2$$

Use a computer algebra system to find the derivative of the function. Use the utility to graph the function and its derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeros of the graph of the derivative. \

$$y=\tan \sqrt{1-x}$$

Slope Fields Use a computer algebra system to graph the slope field for the differential equation and graph the solution satisfying the specified initial condition.

$$\frac{dy}{dx}=\frac{10}{x \sqrt{x^2-1}},\ y(3)=0$$

Write a double integral that represents the surface area of $z=f(x, y)$ over the region $R$. Use a computer algebra system to evaluate the double integral.

$f(x, y)=4-x^2-y^2$ $R=\{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\}$

Use a computer algebra system to (a) find or evaluate the integral and (b) graph two antiderivatives. (c) Describe the relationship between the graphs of the antiderivatives. $\int_{0}^{5} x^{4}\left(25-x^{2}\right)^{3 / 2} d x$