Investigating Finite Differences in Polynomial FunctionsRecall that for a linear function, the rate ofchange is constant as well as the 1st differenceXy=3x-21stdifference-2-1012-8-5-2214The rate of change for a quadratic function is variable,but the second differences are constant.y=-x² + 3x+1X-2-1012-9-31332nddifference difference

Answered: Image /qna-images/answer/8f742f56-2056-410d-bb25-d9076bdac15b.jpg

Answered: Investigating Finite Differences in…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section: Chapter Questions

Problem 2CC: (a) Give the general form of polynomial function P of degree n. (b) What does it mean to say that c...

See similar textbooks

Similar questions

Maximize volume An open box is to be constructed from a piece of cardboard 20 inches by 24 inches by cutting a square of length x from each corner and folding up the sides as shown in the figure. a. Write a polynomial function V(x) that expresses the volume of the constructed box as a function of x. b. Use the theory learned about graphing polynomial functions and graph V(x). c. What is the domain of the function as it relates to the application problem? d. Use a graphing calculator to graph the function, and estimate the value of x that gives the maximum volume and then estimate the maximum volume. Round to one decimal place.
Modeling Polynomials Sketch the graph of a fifth-degree polynomial function that has a zero of multiplicity 2and a negative leading coefficient. Sketch the graph of another polynomial function with the same characteristics except that the leading coefficient is positive.
Modeling Polynomials Sketch the graph of a fourth-degree polynomial function that has a zero of multiplicity 2 and a negative leading coefficient. Sketch the graph of another polynomial function with the same characteristics except that the leading coefficient is positive.
Torricelli's Law Water in a tank will out of a small hole in the bottom when tank is nearly full than when it is nearly empty. According to Torricelli's Law, the Height h(t) of water remaining at time t is a quadratic function of t. A certain tank is filled with and allowed to drain. The height of Water is measured at different times as shown in the table. (a) Find the quadratic polynomial that best fits data. (b) Draw a graph of the polynomial from part(a) together With a scatter plot of the data. (c) Use your graph from part (b) to estimate how long it takes for the tank to drain completely.
Local extrema these exercises involve local maximaand minima of polynomial functions. Graph the function P(x)=(x2)(x4)(x5) and determine how many local extrema it has. If a < b < c, explain why the function P(x)=(xa)(xb)(xc) must have two local extrema-
Height of a basketball The path of a basketball thrown from the free throw line can be modeled by the quadratic function f(x)=0.06x2+1.5x+6, where x is the horizontal distance in feet from the free throw line and f(x) is the height in feet of the ball. Find the maximum height of the basketball.
Think About It Sketch the graph of a fifth-degree polynomial function whose leading coefficient is positive and that has a zero at x=3of multiplicity 2.
Poiseuilles Law for Rate of Fluid Flow Poiseuilles law for the rate of flow of a fluid through a tube is a fourth-order polynomial that is also a power function: F=cR4, where F is the flow rate measured as a volume per unit time, c is a constant, and R is the radius of the tube. a. Assume that R increases by 10. Explain why F increases by 46.41. Hint: Consider 1.10 raised to the fourth power. b. What is the flow rate through a 3/4inch pipe compared with that through a 1/2inch pipe? c. Suppose that an artery supplying blood to the heart muscle see Figure 5.86 is partially blocked and is only half its normal radius. What percentage of the usual blood will flow through the partially blocked artery?
Number of Intercepts and Local Extrema How many x-intercepts and how many local extrema does the polynomial P(x)=x34x have? How many x-intercepts and how many local extremadoes the polynomial Q(x)=x3+4x have? If a > 0. bow many x-intercepts and how many local extrema does each Of the polynomials P(x)=x3ax and Q(x)=x3+ax have? Explain your answer.
(a) Give the general form of polynomial function P of degree n. (b) What does it mean to say that c is a zero of P? Give two equivalent conditions that tell us that c is a zero of P.

Recommended textbooks for you

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781337282291

Author:

Ron Larson

Publisher:

Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781305115545

Author:

James Stewart, Lothar Redlin, Saleem Watson

Publisher:

Cengage Learning

College Algebra

Algebra

ISBN:

9781337282291

Author:

Ron Larson

Publisher:

Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:

9781337278461

Author:

Ron Larson

Publisher:

Cengage Learning

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

Functions and Change: A Modeling Approach to Coll…

Algebra

ISBN:

9781337111348

Author:

Bruce Crauder, Benny Evans, Alan Noell

Publisher:

Cengage Learning

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS