91Ó°ÊÓ

Find the absolute extrema of each function, if they exist, over the indicated interval. Also indicate the \(x\) -value at which each extremum occurs. When no interval is specified, use the real numbers, \((-\infty, \infty)\). $$f(x)=2 x-3 ; \quad[-1,1]$$

Find the absolute extrema of each function, if they exist, over the indicated interval. Also indicate the \(x\) -value at which each extremum occurs. When no interval is specified, use the real numbers, \((-\infty, \infty)\). $$f(x)=9-5 x ; \quad[-10,10]$$

Draw a graph to match the description given. Answers will vary. \(G(x)\) has a positive derivative over \((-\infty,-2)\) and (4,7) and a negative derivative over (-2,4) and \((7, \infty)\).

Graph each function. Then estimate any relative extrema. Where appropriate, round to three decimal places. $$ f(x)=3 x^{2 / 3}-2 x $$

Graph each function using a graphing utility. $$ f(x)=\left|\frac{1}{x}-2\right| $$

Graph each function. Then estimate any relative extrema. Where appropriate, round to three decimal places. $$ f(x)=x^{2}(1-x)^{3} $$

Graph the function given by \(f(x)=\frac{x^{2}-3}{2 x-4}\). a) Find any \(x\) -intercepts. b) Find the \(y\) -intercept if it exists. c) Find any asymptotes.

Find the absolute extrema of each function, if they exist, over the indicated interval. Also indicate the \(x\) -value at which each extremum occurs. When no interval is specified, use the real numbers, \((-\infty, \infty)\). $$f(x)=2 x-3 ; \quad[-1,5)$$

Find the absolute extrema of each function, if they exist, over the indicated interval. Also indicate the \(x\) -value at which each extremum occurs. When no interval is specified, use the real numbers, \((-\infty, \infty)\). $$f(x)=x^{2 / 3} ; \quad[-1,1]$$

Graph each function. Then estimate any relative extrema. Where appropriate, round to three decimal places. $$ f(x)=x^{2}(x-2)^{3} $$