91Ó°ÊÓ

If the brakes of a car, when fully applied, produce a constant deceleration of 11 feet per second per second, what is the shortest distance in which the car can be braked to a halt from a speed of 60 miles per hour?

Use the Mean Value Theorem to show that \(s=1 / t^{2}\) decreases on any interval to the right of the origin.

Sketch the graph of a function \(f\) that has the following properties: (a) \(f\) is everywhere continuous; (b) \(f(0)=0, f(1)=2\); (c) \(f\) is an even function; (d) \(f^{\prime}(x)>0\) for \(x>0\); (e) \(f^{\prime \prime}(x)>0\) for \(x>0\).

Inflation between 1999 and 2004 ran at about \(2.5 \%\) per year. On this basis, what would you expect a car that would have cost \(\$ 20,000\) in 1999 to cost in \(2004 ?\)

In Problems 29-34, sketch the graph of a continuous function fon \([0,6]\) that satisfies all the stated conditions. \(f(0)=1 ; f(6)=3\); increasing and concave down on \((0.6)\)

Sketch the graph of a function \(f\) that has the following properties: (a) \(f\) is everywhere continuous; (b) \(f(2)=-3, f(6)=1\); (c) \(f^{\prime}(2)=0, f^{\prime}(x)>0\) for \(x \neq 2, f^{\prime}(6)=3\); (d) \(f^{\prime \prime}(6)=0, f^{\prime \prime}(x)>0\) for \(26\).

What constant acceleration will cause a car to increase its velocity from 45 to 60 miles per hour in 10 seconds?

Sketch the graph of a function with the given properties. \(f\) is differentiable, has domain \([0,6]\), reaches a maximum of 6 (attained when \(x=3\) ) and a minimum of 0 (attained when \(x=0\) ). Additionally, \(x=5\) is a stationary point.

A wire of length 100 centimeters is cut into two pieces; one is bent to form a square, and the other is bent to form an equilateral triangle. Where should the cut be made if (a) the sum of the two areas is to be a minimum; (b) a maximum? (Allow the possibility of no cut.)

Find, if possible, the (global) maximum and minimum values of the given function on the indicated interval. $$ H(x)=\left|x^{2}-1\right| \text { on }[-2,2] $$