1 / 13

Related Rates

Related Rates. Lesson 6.5. General vs. Specific. Note the contrast … General situation properties true at every instant of time Specific situation properties true only at a particular instant of time We will consider a rock dropped into a pond … generating an expanding ripple.

lowri
Download Presentation

Related Rates

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. Related Rates Lesson 6.5

  2. General vs. Specific • Note the contrast … • General situation • properties true at every instant of time • Specific situation • properties true only at a particular instant of time • We will consider a rock dropped into a pond … generating an expanding ripple

  3. Expanding Ripple • At the point in time whenr = 8 • radius is increasingat 3 in/sec • That is we are given • We seek the rate that the area is changing at that specific time • We want to know r = 8

  4. r A Solution Strategy • Draw a figure • label with variables • do NOT assign exact values unless they never change in the problem • Find formulas that relate the variables

  5. Solution Strategy • Differentiate the equation with respect to time • Substitute in the given information

  6. Example • Given • Find when x = 3Note: we must differentiate implicitly with respect to t

  7. Example • Now substitute in the things we know • x = 3 • Find other values we need • when x = 3, 32 + y2 = 25 and y = 4

  8. Example • Result

  9. Particle on a Parabola • Consider a particle movingon a parabola y2 = 4x at (1,-2) • Its horizontal velocity(rate of changeof x) is 3ft/sec • What is the vertical velocity,the rate of change of y? •

  10. Particle on a Parabola • Differentiate the original equation implicitly with respect to t • Substitute in the values known • Solve for dy/dt

  11. Draining Water Tank • Radius = 20, Height = 40 • The flow rate = 80 gallons/min • What is the rate of change of the radius when the height = 12?

  12. Draining Water Tank • At this point in timethe height is fixed • Differentiate implicitly with respect to t, • Substitute in known values • Solve for dr/dt

  13. Assignment • Lesson 6.5 • Page 409 • Exercises 1 – 27 odd

More Related