Applications of Derivatives

Curve Sketching Review

Here are some review answers!

Attachments:

File	Description	File size
4.7.review.pdf		198 kB
4.7.warmup.pdf		3562 kB

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4.1 Extreme Values

Resources

• Notes

Assignment

• p184 #1-33

Attachments:

File	Description	File size
4.1.notes.pdf		556 kB

4.2 Critical Points

Resources

• Notes

Assignment

• p184 #35-51

Attachments:

File	Description	File size
Unit 4.2 Critical Points notes2.pdf		258 kB

4.3 Mean Value Theorem

Resources

• Notes: Increasing and Decreasing Functions
• Notes; Mean Value Theorem

Assignment

• p192 #1-23, 39-41

Attachments:

File	Description	File size
4.3.a.notes.pdf	Increasing and Decreasing Functions	242 kB
4.3.mvt.notes.pdf	Mean Value Theorem	192 kB

4.4 Antiderivatives

The process of antidifferentiation takes a derivative, and asks, "What would original function would you differentiate to make this derivative?"  You will not be able to find the original function unless a coordinate is provided, as each anti-derivative includes a constant C.  However, we can still find important features of the function, such as where extrema occur, or where points of inflection may occur.  Today we will start looking at graphing functions based on information obtained from the first and second derivatives.

Resources:

• Notes

Assignment:

• p192 #25-37, 43, 45, 47, 51

Things you should know after today:

• given f'(x), determine the antiderivative
• given f'(x) and a coordinate on f(x), determine the antiderivative inculding the constant term

Attachments:

File	Description	File size
4.4.notes.pdf		363 kB
4.5.notes.pdf		4658 kB

4.5 Relating the graphs of f, f` and f``

The process of antidifferentiation takes a derivative, and asks, "What would original function would you differentiate to make this derivative?"  You will not be able to find the original function unless a coordinate is provided, as each anti-derivative includes a constant C.  However, we can still find important features of the function, such as where extrema occur, or where points of inflection may occur.  Today we will start looking at graphing functions based on information obtained from the first and second derivatives.

Resources:

• Notes

Assignment:

• p203 #1-29

Things you should know after today:

• determine where a function is increasing/decreasing
• determine concavity of a function
• determine the location of extrema
• determine inflection points

Attachments:

File	Description	File size
4.5.notes.pdf		4658 kB

4.8 Optimization Problems

One of the applications of derivatives is to use critical points to identify extrema.  This is often related to finding maximum or minimum values in applications.  While you should determine whether the extrema found is a maximum or minimum, sometimes it is not strictly necessary because in the context of the problem, the type of extrema identified by your critical point is obvious.

Resources:

• Notes

Assignment:

• p214 #1-20
• p216 #25-27, 31-35, 37
• p218 #41, 42, 47-49, 53

Attachments:

File	Description	File size
4.10.notes.a.pdf		372 kB
4.8.notes.b.pdf		399 kB
4.8.notes.c.pdf		522 kB