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Graphs and Functions

Finding the derivative of a function given graphically

For the function of f, given below in graph (a) Sketch (b) Where does change its sign (c) Where does have local minima and maxima Using the graph of write a brief description of complete sentences to describe the relationship between the following features of the function of: (a) the local maxima and minima o

Find Domain, Graph, Height, Minimum Surface Area of a Box

Consider an open-top box with a square base and a volume of 108 cubic inches. Let x be the length of a side of the base. a) Calculate the height h as a function of x. Is this function even, odd, or neither? b) What is the domain of the function above? (Note that there may be physical and/or mathematical restrictions.)

Functions, Roots, Convergence, Fixed Point Method

Consider the function f(x) = 2sinx + e^-x - 1 on the interval r E [?2,2]. If you plot the function, you will see that it has two roots on this interval (a) Write down a first order fixed point method for finding one of the two roots. (b) Will this fixed point method converge for both of the roots (Justify)? If it does not co

Minimum spanning tree

Hi. Is the statement below TRUE or FALSE. Why? Question : I have a connected weighted undirected graph G with a minimum spanning tree T. If I increase the weight of one edge, the new minimum spanning tree T' of the new graph G' differs from T in at most one edge.

Business - monthly revenue achieved by selling x boxes of candy...

The monthly revenue achieved by selling x boxes of candy is figured to be x(5 - 0.05x) dollars. The wholesale cost of each box of candy is $1.50. a) How many boxes must be sold each month to achieve a profit of at least $60? b) Using a graph in utility, graph the revenue function. c) What is the maximum re

Constructing an Open Box : Writing Functions and Calculating and Minimizing Area

A open box with a square base is required to have a volume of 10 cubic feet. a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base. b) How much material is required for a base 1 foot by 1 foot? c) How much material is required for a base 2 feet by 2 feet? d) Gr

Functions and Graphs

Trying to find the number of deaths in the United States due to each of the following medical conditions in each of these years; 1985, 1990, 1995, and 2002. heart disease, cancer and aids. How do I plot the data for each disease as points in a rectangular coordinate system? I must connect the data points. Using a curve how

Graphing and Solving Quadratic Inequalities (3 Problems)

State the solution set using interval notation and graph the solution set. Please check these for me and graph them. I do not know how to use a graphing tool. If you also have any advice on how & what tool I can use to graph, it would be helpful. Please do not handwrite the Graphs because I can not view scanned photos

Identifying the set that contains the given number

Define then; Let W = the set of whole numbers F = the set of (non-negative) Fractions I = the set of integers Q= the set of rational numbers R =the set of real numbers Question List all of the sets that have the following properties. (a) 5 is an element of the set(s)? (b) -1/2 is an e

Relations, Functions and Reversal of Variables : Real World Applications

In the real world, what might be a situation where it is preferable for the data for form a relation but not a function? All I found was Edgar Cobb who invented the relational module while working at IBM in the late 1960's. Am I on the right track? Help? When might a reversal of variables be useful in the real world?

Quadratic Equation

A square picture is mounted in a frame 1 cm wide. The area of the picture is 2/3 of the total area. Find the length of a side of the picture.

Function solutions

2. Given the polynomial f(x) = 2x 3 -5x2-4x+3, find the solutions if the function is completed as a) f(x) =0 b) f(x+2)=0 d) f(2x) = 0

Prove A Variation of Fermat's Theorem

There always exists a real number n such that a^n = b^n + c^n , where a, b and c are any integers. The problem is not Fermat's Last Theorem, but a variation of it with real exponents.

Functions: Onto and One-to-one, Bijections and Functions

Please help with the following problems on graphs and functions. Provide step by step calculations. 1. Assuming A,B not equal to no solution, define m1:AxB->A and m2:AxB-> as follows: m1(x,y)=x and m2(x,y)=y. If f: A->B, show that a) f onto=>m2 |f is onto b)f one-to-one=>m2 f is one-to-one 2. Assuming f: A->B and g:

Functions and Graphs: Trends and Real World Implications

Plot your data for each disease as points in a rectangular coordinate system. Year...................1985..........1990..........1995......2002 Heart Disease 771,169 720,058 684,462 162,672 Cancer 461,563 505,322 554,643 557,271 AIDS * 8,000 25,188 39,979 14,095 - Use individu

Plotting a Surface Function

Consider the function u(x,t) = sin(4 pi x) e^(-pi t). Plot using a graphical tool and explain what you observe. Please see the attached file for the fully formatted problems.


What is the "causal relationship" between independent and dependent variable?