Concept explainers
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
b. Use the theory learned about graphing polynomial functions and graph
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.
Trending nowThis is a popular solution!
Chapter 4 Solutions
College Algebra (MindTap Course List)
- Determine the and behavior of the polynomial function. f(x)=8x33x2+2x4arrow_forwardSocial Security Assets The table gives actual and projected year end assets in Social Security trust funds, in trillions of current dollars, where Year represents the number of years since 2000. Source: Social Security Administration. The polynomial function defined by f(t)=0.0000329t30.00450t2+0.0613t+2.34 models the data quite well. a. To verify the fit of the model, find f(10),f(20), and f(30). b. Use a graphing calculator with a command such as nDeriv to find the slope of the tangent line to the graph of f at the following t-values: 0,10,20,30, and 35. c. Use your results in part b to describe the graph of f and interpret the corresponding changes in Social Security assets. YearTrillionsofDollars102.45202.34301.03400.57501.86arrow_forwardExplain why a polynomial function of odd degree must have at least one zero.arrow_forward
- 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.arrow_forwardGraph the quadratic function f(x)=2x24x3 first using the properties as we did in the last section and then graph it using transformations. Which method do you prefer? Whyarrow_forwardFind the zeros of each polynomial function. a. f(x)=x3x22x b. f(x)=2x4+2x2arrow_forward
- (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.arrow_forwardWhat can we conclude if, in general, the graph of apolynomial function exhibits the following endbehavior? As x,f(x) and as x,f(x).arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage