# Applications of Derivatives

## 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

## 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

## 4.12 Related Rate Problems

Another application of derivatives is to solve problems where one rate is desired, and can be calculated using other rates, similar to the way that chain rule is used to find the derivative for a composite function.  We can do this by thinking of each derivative as a combination of differentials, and determine what differentials we need to find the rate that we're looking for.

Resources

• Notes

Assignment

• p237 #1-15
• p238 #17-25, 27
• p240 #29-37