About This Chapter
How It Works:
- Identify the lessons in OUP Introducing Differential Calculus chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the differential calculus topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
You'll learn all of the math topics covered in the textbook chapter, including:
- Slopes and rate of change
- Calculation of derivatives of polynomial equations
- Graphical representations of derivatives
- Determining maximum and minimum values of a graph
- Optimizing simple and complex systems
OUP Oxford IB Math Studies is a registered trademark of Oxford University Press, which is not affiliated with Study.com.
1. Slopes and Rate of Change
If you throw a ball straight up, there will be a point when it stops moving for an instant before coming back down. Consider this as we study the rate of change of human cannonballs in this lesson.
2. Derivatives: Graphical Representations
Take a graphical look at the definitive element of calculus: the derivative. The slope of a function is the derivative, as you will see in this lesson.
3. Calculating Derivatives of Polynomial Equations
Polynomials can describe just about anything and are especially common in describing motion. Learn the tricks to quickly finding the derivatives of these ubiquitous functions.
4. How to Determine Maximum and Minimum Values of a Graph
What is the highest point on a roller coaster? Most roller coasters have a lot of peaks, but only one is really the highest. In this lesson, learn the difference between the little bumps and the mother of all peaks on your favorite ride.
5. Using Differentiation to Find Maximum and Minimum Values
If you are shot out of a cannon, how do you know when you've reached your maximum height? When walking through a valley, how do you know when you are at the bottom? In this lesson, use the properties of the derivative to find the maxima and minima of a function.
6. Optimization and Differentiation
In this lesson, you can learn what optimization means from a mathematical standpoint. Using the techniques taught in this lesson, you can use the five steps to optimization to figure out practical things, like how much sleep you need to get before an exam.
7. Optimizing Simple Systems
Optimization problems may seem overwhelming, but they can actually be quite simple. In this lesson, learn how to use a handy five-step formula to tackle these daunting problems.
8. Optimizing Complex Systems
In this lesson, you'll learn how to follow a five-step process to solve complex optimization problems by visualizing, defining, writing an equation, finding the minimum or maximum, and answering the question.
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Other chapters within the OUP Oxford IB Math Studies: Online Textbook Help course
- OUP Oxford IB Math Studies Chapter 1: Number & Algebra 1
- OUP Oxford IB Math Studies Chapter 2: Descriptive Statistics
- OUP Oxford IB Math Studies Chapter 3: Geometry & Trigonometry 1
- OUP Oxford IB Math Studies Chapter 4: Mathematical Models
- OUP Oxford IB Math Studies Chapter 5: Statistical Applications
- OUP Oxford IB Math Studies Chapter 7: Number & Algebra 2
- OUP Oxford IB Math Studies Chapter 8: Sets & Probability
- OUP Oxford IB Math Studies Chapter 9: Logic
- OUP Oxford IB Math Studies Chapter 10: Geometry & Trigonometry 2
- OUP Oxford IB Math Studies Chapter 13: Prior Learning