91Ó°ÊÓ

Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer correct to two decimal places. $$ g(x)=x^{4}-2 x^{3}-11 x^{2} $$

\(51-58\) Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. $$ y=3 x^{5}-5 x^{3}+3, \quad[-3,3] \text { by }[-5,10] $$

\(51-58\) Graph the polynomial in the given viewing rectangle. Find the coordinates of all local extrema. State each answer rounded to two decimal places. $$ y=x^{5}-5 x^{2}+6, \quad[-3,3] \text { by }[-5,10] $$

\(57-58\) . Show that the given value(s) of \(c\) are zeros of \(P(x),\) and find all other zeros of \(P(x) .\) $$ P(x)=3 x^{4}-x^{3}-21 x^{2}-11 x+6, \quad c=\frac{1}{3},-2 $$

Find all zeros of the polynomial. \(P(x)=x^{4}-x^{2}+2 x+2\)

A polynomial \(P\) is given. (a) Find all the real zeros of \(P\) (b) Sketch the graph of \(P\) . $$ P(x)=-x^{3}-2 x^{2}+5 x+6 $$

Find the intercepts and asymptotes, and then sketch a graph of the rational function and state the domain and range. Use a graphing device to confirm your answer. $$ r(x)=\frac{2 x^{2}+2 x-4}{x^{2}+x} $$

Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer correct to two decimal places. $$ g(x)=x^{5}-8 x^{3}+20 x $$

Find the local maximum and minimum values of the function and the value of x at which each occurs. State each answer correct to two decimal places. $$ U(x)=x \sqrt{6-x} $$

Find the intercepts and asymptotes, and then sketch a graph of the rational function and state the domain and range. Use a graphing device to confirm your answer. $$ r(x)=\frac{x^{2}-x-6}{x^{2}+3 x} $$