91Ó°ÊÓ

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, use the real line, \((-\infty, \infty)\). $$f(x)=x^{2}+\frac{432}{x} ; \quad(0, \infty)$$ (GRAPH CAN'T COPY)

Since \(1970,\) the purchasing power of the dollar, as measured by consumer prices, can be modeled by the function $$P(x)=\frac{2.632}{1+0.116 x}$$, where \(x\) is the number of years since \(1970 .\) (Source: U.S. Bureau of Economic Analysis.) a) Find $$P(10), P(20),$$ and $$P(40)$$ b) When was the purchasing power $$\$ 0.50 ?$$ c) Find $$\lim _{x \rightarrow \infty} P(x)$$. (GRAPHS CANNOT COPY)

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, use the real line, \((-\infty, \infty)\). $$f(x)=x^{2}+\frac{250}{x} ; \quad(0, \infty)$$ (GRAPH CAN'T COPY)

I.ook up "differential" in a book or Web site devoted to math history. In a short paragraph, describe your findings.

Draw a graph to match the description given. Answers will vary. \(f(x)\) is increasing over \((-\infty, 2)\) and decreasing over \((2, \infty)\)

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). $$f(x)=2 x^{4}-x ;[-1,1]$$

Draw a graph to match the description given. Answers will vary. \(g(x)\) is decreasing over \((-\infty,-3)\) and increasing over \((-3, \infty)\)

Draw a graph to match the description given. Answers will vary. \(G(x)\) is decreasing over \((-\infty, 4)\) and \((9, \infty)\) and increasing over (4,9)

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, \((-\infty, \infty)\). $$f(x)=\sqrt[3]{x} ; \quad[0,8]$$

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, \((-\infty, \infty)\). $$f(x)=\sqrt{x} ; \quad[0,4]$$