1 / 6

Optimization and Differentials (Sections 3.7 and 3.9)

Optimization and Differentials (Sections 3.7 and 3.9). By Brandan Jeter, Zach Young, and Daniel Cotton. Optimization. Optimization is the process of using calculus to determine the maximum or minimum value of a given function.

branden-stanley
Download Presentation

Optimization and Differentials (Sections 3.7 and 3.9)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Optimization and Differentials(Sections 3.7 and 3.9) By Brandan Jeter, Zach Young, and Daniel Cotton

  2. Optimization • Optimization is the process of using calculus to determine the maximum or minimum value of a given function. • For example, you’re given the surface area of a cube, and you want to find the maximum volume of that cube.

  3. Optimization Guidelines • 1. Identify all given quantities and quantities to be determined. • 2. Write a primary equation for the quantity that is to be maximized or minimized. • 3. Reduce the primary equation to one having a single independent variable. This may involve using secondary equations. • 4. Determine the desired maximum or minimum by finding the derivative.

  4. Differentials • dy=f’(x)dx • d(cu)=c du • d(u±v)=du±dv • D(uv)=udv+vdu • D(u/v)=(vdu-udv)/v2

  5. Error Propagation • For example, the radius of a ball is .7 inches with an error within .01 inches. Estimate the propagated error of the volume of the ball. • V=(4/3)r3 • dV=4 r2dr • =4 (0.7)(±0.01) • =±0.0616 cubic inches

  6. Additional Resources • Optimization • http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx • http://www.qcalculus.com/cal08.htm • Differentials • http://tutorial.math.lamar.edu/Classes/CalcI/Differentials.aspx • http://www.cliffsnotes.com/study_guide/Differentials.topicArticleId-39909,articleId-39898.html

More Related