# Applications of Derivatives

## 4.1 Extreme Values

Resources

• Notes

Assignment

• p184 #1-33
Attachments:
FileDescriptionFile size
4.1.notes.pdf 556 kB

## 4.3 Mean Value Theorem

Resources

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

Assignment

• p192 #1-23, 39-41
Attachments:
FileDescriptionFile size
4.3.a.notes.pdfIncreasing and Decreasing Functions242 kB
4.3.mvt.notes.pdfMean Value Theorem192 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:
FileDescriptionFile 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:
FileDescriptionFile 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:
FileDescriptionFile size
4.10.notes.a.pdf 372 kB
4.8.notes.b.pdf 399 kB
4.8.notes.c.pdf 522 kB

## 4.10 Linear Approximation - Newton's Method

Your calculator uses calculus to find out values for things like sine, logs and roots.  Today, you will see how many of these complex values can be determined with only a regular calculator.

Resources

• Notes

Assignment:

• p229 #1-17, 37, 51
Attachments:
FileDescriptionFile size
4.10.notes.a.pdf 372 kB
4.10.notes.b.pdf 378 kB

## 4.11 Differentials

We can estimate the amount of change in a function using a derivative.  We can think of the derivative,

as measuring the change in y and the change in x for very small differences in y and x.  This can be used for determining how much a function changes, provided that the numbers are very small.

Resources

• Notes

Assignment

• p229 #19-35, 39-45
Attachments:
FileDescriptionFile size
4.11.notes.pdf 389 kB