91Ó°ÊÓ

Use the Upper and Lower Bound Theorem to solve Exercises \(1-4\). Show that all the real roots of the equation \(2 x^{3}+5 x^{2}-8 x-7=0\) lie between \(-4\) and 2.

Use the Upper and Lower Bound Theorem to solve Exercises \(1-4\). Show that all the real roots of the equation \(2 x^{5}-13 x^{3}+2 x-5=0\) lie between \(-3\) and 3.

a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the root from part (b) and solve the equation. $$ x^{3}-2 x^{2}-11 x+12=0 $$

Determine the constant of variation for each stated condition. \(A\) varies directly as \(B\) and inversely as \(C,\) and \(A=9\) when \(B=12\) and \(C=4\)

In Exercises \(21-26,\) use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$f(x)=11 x^{3}-6 x^{2}+x+3$$

In Exercises \(21-26,\) use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$f(x)=-11 x^{4}-6 x^{2}+x+3$$

In Exercises \(29-36,\) find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. \(n=3 ; 4\) and \(2 i\) are zeros; \(f(-1)=-50\)

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. $$f(x)=-2 x^{4}+2 x^{3}$$

Use the four-step procedure for solving variation problems given on page 356 to solve. The volume of a gas varies directly as its temperature and inversely as its pressure. At a temperature of 100 Kelvin and a pressure of 15 kilograms per square meter, the gas occupies a volume of 20 cubic meters. Find the volume at a temperature of 150 Kelvin and a pressure of 30 kilograms per square meter.

The width of a rectangular box is twice the height and the length is 7 inches more than the height. If the volume is 72 cubic inches, find the dimensions of the box. (GRAPH CANNOT COPY).