## Grade 12 Calculus and Vectors

Chapter 3: Applications of derivatives

All students must remember** “CONDITIONS” **when working on application problems. Aside from noting the givens, students should be thinking about, "CONDITIONS," "CONDITIONS," and "CONDITIONS!" It is especially important to remember conditions that give you** ZEROES! **Zeroes will become your favourite number (if it isn’t already) simply because they make your calculations easier by dropping out or disappearing from the equations.

Having said that, let’s list a few tricks and CONDITIONS that works well for problems related to this chapter:

1. When you are completely lost during a test or quiz (in calculus only) take the derivative, you really can't go wrong. (Please do not take derivative in a biology quiz or test and complain about irrelevance. We really can’t help you at that point)

2. Label the origin (0,0) as your start point, be it a displacement graph, velocity graph, acceleration graph or any other graph you can think off. It really helps to simplify your calculations at this level. Also, always define your positive (+ve) and negative (-ve) axes (direction). This will further simplify when analysing the problem.

3. The above labelling strategy will already give you a ZERO value for your CONDITIONS. That is, your initial displacement is ZERO, which could be used in the expression you have as the POSITION FUNCTION.

4. Velocity has to equal to ZERO as the object comes to a stop or halt, BEFORE the object in question changes direction to head toward its initial point. Exception is made when the object simply makes a small change in the direction of travel, or uses a semicircular path to turn around. In a nut-shell, if the words from the second sentence does not show up in your question, start looking for that ZERO. The values found through first derivative being set to ZERO are called critical numbers, points or values. Usually, this is how velocity will be found in this chapter.

5. Acceleration is negative (-ve) during a "slow-down" or deceleration of the object in question.

6. Acceleration is ZERO when the object is on a "cruise" mode or at a state of constant motion (inertial) or at "rest."

Can you remember these conditions?

You will know this like the back of your hand after you have attempted a few questions. Yes, thats right, you have to do homework. The benefits of doing homework is, well if you have not noticed it already, you will be a lot faster with answering questions during quizes, tests and exams.* You bet your last coin on that, not ours! Please. *

**
3.1 Higher order Derivatives - Position, Velocity, and Acceleration
3.2 Extreme Value Problems - Local and Absolute Maxima and Minima
3.3 Optimization Problems - Distances, Areas, Volumes, Velocity & more
3.4 Optimization Problems with Economics and Science
**

## Grade 12 Calculus and Vectors

Chapter 1: Introduction to* Calculus *and Vectors

Chapter 2: Derivatives

Chapter 3: Applications of Derivatives

3.1 Higher order Derivatives

Position, Velocity, and Acceleration

3.2 Extreme Value Problems

Local and Absolute Maxima and Minima

3.3 Optimization Problems

Distances, Areas, Volumes, Velocity &more

3.4 Optimization Problems - Economics and Science

Chapter 4: Curve Sketching

Chapter 5: Derivatives of Trigonometric Functions

Chapter 6: Derivatives of Exponential Functions

Chapter 7: Introduction to * Vectors *

Chapter 8: Vector Operations and Applications

Chapter 9: Equations of Lines

Chapter 10: Equations of Planes

Chapter 11: Points, Lines and Planes

Videos for each topic contain a playlist, allowing you to choose the instructor and learning style to your liking. You can choose different videos in a topic by placing the mouse over the video and selecting a different video from the playlist. Videos of solutions to multiple example problems are also available to illustrate to students how each tools and techniques should be used.

Please refer to high school math prerequisite tree to see the recommended courses and materials one should be familiar with prior to taking up Calculus and Vectors.

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