91Ó°ÊÓ

Assume that \(f\) is differentiable over \((-\infty, \infty) .\) Classify each of the following statements as either true or false. If a statement is false, explain why. If \(f\) has two points of inflection, then there is a critical value located between those points of inflection.

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

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

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)

Assume that \(f\) is differentiable over \((-\infty, \infty) .\) Classify each of the following statements as either true or false. If a statement is false, explain why. The function \(f\) can have a point of inflection at a critical value.

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

Graph each function using a graphing utility. $$ f(x)=x^{2}+\frac{1}{x^{2}} $$

Graph each function using a graphing utility. $$ f(x)=\frac{x}{\sqrt{x^{2}+1}} $$

Draw a graph to match the description given. Answers will vary. \(F(x)\) is increasing over \((-\infty, 5)\) and \((12, \infty)\) and decreasing over (5,12)

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