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Chapter 4: Q. 48 (page 194)
In Problems 41鈥� 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.
The polynomial function iswith degree 3.
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In Problems 49鈥� 60, for each polynomial function:
(a) List each real zero and its multiplicity.
(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of f resembles for large values of
Solve the inequality . Graph the solution set.
In Problems 63鈥�72, find the real solutions of each equation.
United Parcel Service has contracted you to design a closed box with a square base that has a volume of cubic inches. See the illustration.
Part (a): Express the surface area S of the box as a function of x.
Part (b): Using a graphing utility, graph the function found in part (a).
Part (c): What is the minimum amount of cardboard that can be used to construct the box?
Part (d): What are the dimensions of the box that minimize the surface are?
Part (e): Why might UPS be interested in designing a box that minimizes the surface area?
In Problems 39鈥�56, find the real zeros of f. Use the real zeros to factor f.
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