The second derivative

Differentiating a derivative to read concavity: where a graph bends upward or downward, and what the units of a rate of change of a rate of change mean.

Active Calculus, The second derivative

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2 exercises

Activity 1.6.3

A potato is placed in an oven whose temperature is 350 degrees Fahrenheit, and the potato's temperature $F$ (in degrees Fahrenheit) is recorded in Table. Time $t$ is measured in minutes.

In Activity, we used this data to compute approximations to $F'(20)$ and $F'(40)$ using central differences. Those values are provided in Table, along with several others computed in the same way.

What are the units on $F'(t)$ ? What is the…

2.5

Exercise 12

A bungee jumper's height $h$ (in feet ) at time $t$ (in seconds) is given in part by the table:

Use the given data to estimate $h'(4.5)$ , $h'(5)$ , and $h'(5.5)$ . At which of these times is the bungee jumper rising most rapidly?
Use the given data and your work in (a) to estimate $h''(5)$ .
What physical property of the bungee jumper does the value of $h''(5)$ measure? What are its units?
Based on the data, on what approximate time intervals…

2.5