91Ó°ÊÓ

For each function: a. Make a sign diagram for the first derivative. b. Make a sign diagram for the second derivative. c. Sketch the graph by hand, showing all relative extreme points and inflection points. $$ f(x)=\sqrt[3]{(x-1)^{2}} $$

BUSINESS: Copier Repair A copier company finds that copiers that are \(x\) years old require, on average, \(f(x)=1.2 x^{2}-4.7 x+10.8\) repairs annually for \(0 \leq x \leq 5\). Find the year that requires the least repairs, rounding your answer to the nearest year.

Sketch the graph of each function "by hand" after making a sign diagram for the derivative and finding all open intervals of increase and decrease. \(f(x)=\left(x^{2}-2 x-8\right)^{2}\)

Is it realistic to have a reproduction function that is increasing for all values of \(p>0\), such as \(f(p)=5 p\) or \(f(p)=p^{2} ?\)

For each function: a. Make a sign diagram for the first derivative. b. Make a sign diagram for the second derivative. c. Sketch the graph by hand, showing all relative extreme points and inflection points. $$ f(x)=\sqrt[5]{x+2}+3 $$

If the current price is \(\$ 75\) and you find that profit is maximized when there are \(-5\) price increases of \(\$ 3\), what should the price be?

For each equation, find \(d y / d x\) evaluated at the given values. $$ \sqrt[3]{x}+\sqrt[3]{y}=3 \text { at } x=1, y=8 $$

For each function: a. Make a sign diagram for the first derivative. b. Make a sign diagram for the second derivative. c. Sketch the graph by hand, showing all relative extreme points and inflection points. $$ f(x)=\frac{x}{x^{2}-1} $$

Sketch the graph of each function "by hand" after making a sign diagram for the derivative and finding all open intervals of increase and decrease. \(f(x)=x^{2}(x-4)^{2}\)

GENERAL: Driving and Age Studies have shown that the number of accidents a driver has varies with the age of the driver, and is highest for very young and very old drivers. The number of serious accidents for drivers of age \(x\) during a recent year was approximately \(f(x)=0.013 x^{2}-1.35 x+48\) for \(16 \leq x \leq 85\). Find the age that has the least accidents, rounding your answer to the nearest year.