91Ó°ÊÓ

In Exercises, find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. $$ f(x)=3 x^{2 / 3}-2 x, \quad[-1,2] $$

In Exercises, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. $$ f(x)=x \sqrt{x+1} $$

In Exercises, find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. $$ g(t)=\frac{t^{2}}{t^{2}+3}, \quad[-1,1] $$

In Exercises, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. $$ h(x)=x \sqrt[3]{x-1} $$

In Exercises, find the higher-order derivative. $$ f^{\prime}(x)=2 x^{2} $$

In Exercises, find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. $$ h(t)=(t-1)^{2 / 3}, \quad[-7,2] $$

In Exercises, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. $$ f(x)=x^{4}-2 x^{3} $$

In Exercises, find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. $$ g(x)=4\left(1+\frac{1}{x}+\frac{1}{x^{2}}\right), \quad[-4,5] $$

In Exercises, find the critical numbers and the open intervals on which the function is increasing or decreasing. Then use a graphing utility to graph the function. $$ f(x)=\frac{1}{i} x^{4}-2 x^{2} $$

In Exercises, find the higher-order derivative. $$ f^{\prime \prime}(x)=20 x^{3}-36 x^{2} $$