# patty's calculus videos

## part 3 - applications (10 videos)                      back to playlists

Part 3 - Applications of Derivatives - Video 1
Section 1: Related Rates
Lesson 1: Introduction, the Balloon Example (32:49)

What is a related rates problem? (0:37) A hot air balloon has sprung a leak! We work through Step 1 (label changing quantities) and Step 2 (identify the rate we know and the rate we want) (3:12).

Part 3 - Applications of Derivatives - Video 2
Section 1: Related Rates
Lesson 2: Helicopter and Car Example (36:08)

We turn to a related rates example that involves a helicopter and car, working Step 1 (label the changing quantities) and Step 2 (identify the rate we know and the rate we want) (0:40).

Part 3 - Applications of Derivatives - Video 3
Section 1: Related Rates
Lesson 3: Two Further Examples (54:12)

We turn to two tougher related rates examples. First, we work through an example of water pouring into a conical tank (0:36). Next, we solve an example in which you shoot a video, panning your camera to follow a runner (28:37).

Part 3 - Applications of Derivatives - Video 4
Section 2: How Derivatives Affect the Graph
Lesson 1: Where f is Increasing/Decreasing (53:49)

We begin with a technical definition of increasing and decreasing (0:38). Next, we discover how f'(x) tells us whether f is increasing or decreasing (9:29).

Part 3 - Applications of Derivatives - Video 5
Section 2: How Derivatives Affect the Graph
Lesson 2: Finding Local Maxima and Minima (51:28)

We begin by discussing what we mean by the local maxima and minima (local extrema) of a function (0:38), and we discuss the precise definitions of local max and min (4:44).

Part 3 - Applications of Derivatives - Video 6
Section 2: How Derivatives Affect the Graph
Lesson 3a: Concavity and Inflection Points (1:01:06)

We turn to the idea of the concavity of the graph of a function, and how to use f''(x) to determine the whether f is concave up or concave down (0:37).

Part 3 - Applications of Derivatives - Video 7
Section 2: How Derivatives Affect the Graph
Lesson 3b: Concavity and Inflection Points (52:44)

We begin with further remarks on Example 2, discussing the particular type of local min we found, a cusp, and how this relates to the fact that f'(x) was undefined there (0:41).

Part 3 - Applications of Derivatives - Video 8
Section 3: Optimization Problems
Lesson 1: Intro and Rectangle Example (25:26)

We briefly talk about what we mean by an optimization problem and the steps to set it up (0:38). Example about maximizing the area of a rectangle (12:31).

Part 3 - Applications of Derivatives - Video 9
Section 3: Optimization Problems
Lesson 2: Rectangle Trapped Under Curve (38:17)

A new example involving a rectangle inscribed (trapped) under a curve, working Step 1 (label variables and constants) (0:37), Step 2 (identify the function to maximize or minimize) (7:21), and Step 3 (find constraint equation) (13:11).

Part 3 - Applications of Derivatives - Video 10
Section 3: Optimization Problems
Lesson 3: Constructing the Cheapest Box (34:51)

A final optimization example involving the construction of a rectangular box, working through Step 1 (labeling quantities that vary and those that are constant), Step 2 (identifying the function we want to maximize or minimize) (0:37).