91Ó°ÊÓ

Draw a graph to match the description given. Answers will vary. \(f(x)\) has a positive derivative over \((-\infty, 3)\) and (3,9) a negative derivative over \((9, \infty),\) and a derivative equal to 0 at \(x=3\)

Find the absolute maximum and minimum values 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, is specified, use the real line, \((-\infty, \infty)\). $$f(x)=2 x-3 ; \quad[-1,5)$$

Find each limit, if it exists. $$\lim _{x \rightarrow 1} \frac{x^{3}-1}{x^{2}-1}$$

Find each limit, if it exists. $$\lim _{x \rightarrow-\infty} \frac{7 x^{5}+x-9}{6 x+x^{3}}$$

Find the absolute maximum and minimum values 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, is specified, use the real line, \((-\infty, \infty)\). $$f(x)=9-5 x ;[-2,3)$$

Draw a graph to match the description given. Answers will vary. \(F(x)\) has a negative derivative over \((-\infty,-1)\) and a positive derivative over \((-1, \infty),\) and \(F^{\prime}(-1)\) does not exist.

Find the absolute maximum and minimum values 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, is specified, use the real line, \((-\infty, \infty)\). $$f(x)=x^{2 / 3} ; \quad[-1,1]$$

Find each limit, if it exists. $$\lim _{x \rightarrow-\infty} \frac{2 x^{4}+x}{x+1}$$

Draw a graph to match the description given. Answers will vary. \(G(x)\) has a positive derivative over \((-\infty, 0)\) and \((3, \infty)\) and a negative derivative over \((0,3),\) but neither \(G^{\prime}(0)\) nor \(G^{\prime}(3)\) exists.

$$\text {Graph each function using a calculator, iPlot, or Graphicus.}$$ $$f(x)=x^{2}+\frac{1}{x^{2}}$$