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Chapter 3: Problem 52
What does it mean if two quantities vary inversely?
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What are the zeros of a polynomial function and how are they found?
In Exercises \(27-34,\) find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the \(x\) -axis, or touches the \(x\) -axis and turns around, at each zero. $$f(x)=x^{3}+7 x^{2}-4 x-28$$
In Exercises \(35-50\) a. Use the Leading Coefficient Test to determine the graphs end behavior. b. Find \(x\) -intercepts by setting \(f(x)=0\) and solving the resulting polynomial equation. State whether the graph crosses the \(x\)-axis, or touches the \(x\)-axis and turns around, at each intercept. c. Find the \(y\) -intercept by setting \(x\) equal to 0 and computing \(f(0)\) d. Determine whether the graph has \(y\) -axis symmetry, origin symmetry, or neither. e. If necessary, find a few additional points and graph the function. Use the fact that the maximum number of turning points of the graph is \(n-1\) to check whether it is drawn correctly. $$f(x)=-x^{4}+16 x^{2}$$
In Exercises \(55-56,\) use a graphing utility to determine upper and lower bounds for the zeros of \(f .\) Does synthetic division verify your observations? $$ f(x)=2 x^{4}-7 x^{3}-5 x^{2}+28 x-12 $$
The heat generated by a stove element varies directly as the square of the voltage and inversely as the resistance. If the voltage remains constant, what needs to be done to triple the amount of heat generated?
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