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- Discuss linearization of functions.
- Use linearization to estimate the values of functions.
- Explain Newton's method.
- Find the root of an equation using Newton's method.
- Describe the relationship between optimization and differentiation.
- Optimize simple and complex systems.
1. Linearization of Functions
Over the river and through the woods to Grandmother's house we go ... Are we there yet? In this lesson, apply linearization to estimate when we will finally get to Grandma's house!
2. How to Estimate Function Values Using Linearization
Sometimes landing on Mars isn't that easy. You might need to use linearization to estimate if you will crash into the planet, or miss it entirely. Learn how to do just that in this lesson.
3. What is Newton's Method?
Hang gliding can be perilous, especially if you think you might land in a stinky pigpen. In this lesson, find out how Newton's Method might help you determine whether you'll be covered in mud when you land.
4. How to Use Newton's Method to Find Roots of Equations
Finding the roots of equations usually requires the use of a calculator. However, in this lesson you'll use Newton's Method to find the root of any equation, even when you can't solve for it explicitly.
5. 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.
6. 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.
7. 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 Calculus: Tutoring Solution course
- Graphing and Functions: Tutoring Solution
- Continuity: Tutoring Solution
- Geometry and Trigonometry in Calculus: Tutoring Solution
- Using Scientific Calculators in Calculus: Tutoring Solution
- Limits: Tutoring Solution
- Rate of Change: Tutoring Solution
- Calculating Derivatives and Derivative Rules: Tutoring Solution
- Graphing Derivatives and L'Hopital's Rule: Tutoring Solution
- Area Under the Curve and Integrals: Tutoring Solution
- Integration and Integration Techniques: Tutoring Solution
- Integration Applications: Tutoring Solution
- Differential Equations: Tutoring Solution