# 4: Applications of the Derivative

- Page ID
- 4177

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- 4.1: Newton's Method
- Newton's Methos is a technique to approximate the solution to equations and is built around tangent lines. The main idea is that if x is sufficiently close to a root of f(x), then the tangent line to the graph at (x,f(x) will cross the x-axis at a point closer to the root than x.

- 4.2: Related Rates
- The topic of "related rates" is the approach that knowing the rate at which one quantity is changing can determine the rate at which the other changes.

- 4.3: Optimization
- In this section we apply the concepts of extreme values to solve "word problems," i.e., problems stated in terms of situations that require us to create the appropriate mathematical framework in which to solve the problem.

- 4.4: Differentials
- The differential of x, denoted dx , is any nonzero real number (usually taken to be a small number). The differential of y, denoted dy, is dy=f′(x)dx.

### Contributors

Gregory Hartman (Virginia Military Institute). Contributions were made by Troy Siemers and Dimplekumar Chalishajar of VMI and Brian Heinold of Mount Saint Mary's University. This content is copyrighted by a Creative Commons Attribution - Noncommercial (BY-NC) License. http://www.apexcalculus.com/