Extra Practice Related Ratesap Calculus



Optimization Practice 2, 4, 6, 9, 14 02 - HW Solutions Related Rates Notesheet 04 Completed Notes Related Rates Day 1 Worksheet 04 - HW Solutions Related Rates Online Practice 05 Wall to Post Solution Videos Related Rates Day 2 Worksheet 05 - HW Solutions Related Rates and Optimization Practice 06 - HW Solutions (Coming Soon).

Section 3-11: Related Rates. In this section we are going to look at an application of implicit differentiation. Most of the applications of derivatives are in the next chapter however there are a couple of reasons for placing it in this chapter as opposed to putting it into the next chapter with the other applications. To solve problems with Related Rates, we will need to know how to differentiate implicitly, as most problems will be formulas of one or more variables. But this time we are going to take the derivative with respect to time, t, so this means we will multiply by a differential for the derivative of every variable! AP Calculus Unit #4-Applications of the Derivative Part I Smac Key.pdf Author: sean.mcconnell Created Date: 12/5/2018 12:55:12 PM.

This video lesson explores the concept of Related Rates, which is the study of what is happening over time.

Extra

To solve problems with Related Rates, we will need to know how to differentiate implicitly, as most problems will be formulas of one or more variables.

But this time we are going to take the derivative with respect to time, t, so this means we will multiply by a differential for the derivative of every variable!

But don’t let this confused you, as there are only four basic steps when problem-solving with Related Rates:

  1. Write down every given information or quantity, even what you’re looking for, and make a sketch.
  2. Determine the equation needed to solve for your unknown quantity.
  3. Take the derivative implicitly, not forgetting to multiply by your differential for every single variable!
  4. Plug in all of your given information or quantities and solve.

And here’s a big hint…

Extra practice related ratesap calculus calculator

…most of the time all we have to do is find an equation that relates the rate we’re looking for to a rate that we already know, as Paul’s Online Notes so nicely states.

This means we need to look for geometric shapes, known formulas, and ratios.

Ladder Sliding Down a Wall

Together we will solve these 8 classic questions:

  • Pebble Dropped In Pond
  • Air Being Pumped Into A Balloon
  • Edges Of Cube Expanding
  • Radar Tracking Station & Airplane Flight Path
  • Sand Falling onto a Conical Pile
  • Water Pouring into a Conical Tank
  • Boat Pulled into a Dock
  • Ladder Sliding Down a Wall
Related

How to Solve Related Rates – Video

1 hr 35 min

  • Overview of Related Rates + Tips to Solve Them
  • 00:02:58 – Increasing Area of a Circle
  • 00:12:30 – Expanding Volume of a Sphere
  • 00:21:15 – Expanding Volume of a Cube
  • 00:26:32 – Calculate the Speed of an Airplane
  • 00:39:13 – Conical Sand Pile
  • 00:51:19 – Conical Water Tank
  • 00:59:59 – Boat & Winch
  • 01:09:13 – Ladder Sliding Down A Wall

Related Rates

Extra Practice Related Ratesap Calculus


Related Rates – 2 Examples

Get access to 6 more examples and over 150 HD videos with your subscription

Monthly, Half-Yearly, and Yearly Plans Available

Calculus

Not yet ready to subscribe? Take Calcworkshop for a spin with our FREE limits course