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Chapter 2: Problem 91
Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$g(x)=5 x^{5}-10 x$$
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The revenues \(R\) (in millions of dollars) for a company from 2003 through 2010 can be modeled by \(R=6.212 t^{3}-132.87 t^{2}+863.2 t-1115,3 \leq t \leq 10\) where \(t\) represents the year, with \(t=3\) corresponding to 2003 (a) Use a graphing utility to approximate any relative extrema of the model over its domain. (b) Use the graphing utility to approximate the intervals on which the revenue for the company is increasing and decreasing over its domain. (c) Use the results of parts (a) and (b) to describe the company's revenue during this time period.
Use a graphing utility to graph the equation. Use the graph to approximate the values of \(x\) that satisfy each inequality. Equation \(y=-x^{2}+2 x+3\) Inequalities (a) \(y \leq 0\) (b) \(y \geq 3\)
(a) state the domain of the function, (b) identify all intercepts, (c) find any vertical or horizontal asymptotes, and (d) plot additional solution points as needed to sketch the graph of the rational function. $$g(x)=\frac{1}{6-x}$$
(a) Find the interval(s) for \(b\) such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients. $$2 x^{2}+b x+5=0$$
Fill in the blanks. The graphs of all polynomial functions are _______, which means that the graphs have no breaks, holes, or gaps.
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