91Ó°ÊÓ

WRITING Let \(f(x)=13\). State the degree, type, and leading coefficient. Describe the end behavior of the function. Explain your reasoning.

Graph the function. Identify the \(x\)-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing. $$h(x)=x^4-3 x^2+x$$

s 27–32, fi nd the product of the binomials \((x-5)(x+2)(x-6)\)

Graph the function. Identify the \(x\)-intercepts and the points where the local maximums and local minimums occur. Determine the intervals for which the function is increasing or decreasing. $$h(x)=x^5+2 x^2-17 x-4$$

In Exercises 25–32, use synthetic division to evaluate the function for the indicated value of x. $$ f(x)=x^3-6 x+1 ; x=6 $$

Find all the real solutions of the equation. \(2 x^3-3 x^2-50 x-24=0\)

PROBLEM SOLVING A portion of the path that a hummingbird flies while feeding can be modeled by the function $$ f(x)=-\frac{1}{5} x(x-4)^2(x-7), 0 \leq x \leq 7 $$ where \(x\) is the horizontal distance (in meters) and \(f(x)\) is the height (in meters). The hummingbird feeds each time it is at ground level. a. At what distances does the hummingbird feed? b. A second hummingbird feeds 2 meters farther away than the first hummingbird and flies twice as high. Write a function to model the path of the second hummingbird.

In Exercises 25–32, use synthetic division to evaluate the function for the indicated value of x. $$ f(x)=-x^4-x^3-2 ; x=5 $$

The profit \(P\) (in millions of dollars) for a DVD manufacturer can be modeled by \(P=-6 x^3+72 x\), where \(x\) is the number (in millions) of DVDs produced. Use synthetic division to show that the company yields a profit of \(\$ 96\) million when 2 million DVDs are produced. Is there an easier method? Explain.

Sketch a graph of a polynomial function \(f\) having the given characteristics. \- The graph of \(f\) has \(x\)-intercepts at \(x=-4, x=0\), and \(x=2\). \- \(f\) has a local maximum value when \(x=1\). \- \(f\) has a local minimum value when \(x=-2\).