Slope functions Determine the slope function S (x) for the following functions
$\text{ƒ}\left(x\right)=\mid x\mid$

Velocity from position The graph of $s=f\left(t\right)$ represents the position of an object moving along a line at time $t\ge 0$ . <IMAGE>

a. Assume the velocity of the object is 0 when $t=0$ . For what other values of t is the velocity of the object zero?

Velocity from position The graph of $s=f\left(t\right)$ represents the position of an object moving along a line at time $t\ge 0$ . <IMAGE>

c. Sketch a graph of the velocity function.

Fish length Assume the length L (in centimeters) of a particular species of fish after t years is modeled by the following graph. <IMAGE>

b. What does the derivative tell you about how this species of fish grows?

Evaluating functions from graphs Assume ƒ is an odd function and that both ƒ and g are one-to-one. Use the (incomplete) graph of ƒ and g the graph of to find the following function values. <IMAGE>

ƒ(g(4))

Let ƒ(x) = 1/ (x³+1).

Compute ƒ(2) and ƒ(y²).

The National Weather Service releases approximately $70,000$ radiosondes every year to collect data from the atmosphere. Attached to a balloon, a radiosonde rises at about $1000$ ft/min until the balloon bursts in the upper atmosphere. Suppose a radiosonde is released from a point $6$ ft above the ground and that $5$ seconds later, it is $83$ ft above the ground. Let $f\left(t\right)$ represent the height (in feet) that the radiosonde is above the ground $t$ seconds after it is released. Evaluate $\frac{f\left(5\right)-f\left(0\right)}{5-0}$ and interpret the meaning of this quotient.

A GPS device tracks the elevation $E$ (in feet) of a hiker walking in the mountains. The elevation $t$ hours after beginning the hike is given in the figure. <IMAGE>

Find the slope of the secant line that passes through points $A$ and $B$. Interpret your answer as an average rate of change over the interval $1\leq{t}\leq{3}$.

A GPS device tracks the elevation $E$ (in feet) of a hiker walking in the mountains. The elevation $t$ hours after beginning the hike is given in the figure. <IMAGE>

Repeat the procedure outlined in part (a) for the secant line that passes through points $P$ and $Q$.