# Ch 10: Applications of Derivatives

Watch enlightening video lessons about applications of derivatives. Learn about optimizing simple and complex systems, Newton's method, differentiation and more.

## Applications of Derivatives

If you've been studying calculus and learned what derivatives are, now you can learn what to do with them. How can they be useful in solving math problems and, perhaps more importantly, in real life? Derivatives have a wide variety of useful purposes that you'll learn about in these lessons.

For example, in these lessons on the applications of derivatives, you'll learn about the linearization of functions. Essentially, this boils down to finding the linear approximation of a function at a particular point. You'll delve deeper in a related lesson, where you'll learn about estimating the value of a function using linearization.

Then there's Isaac Newton and the tool that's come to be known as Newton's method. In some situations, you'll want to know the root of an equation. In other words, you'll be trying to find f(x) = 0. Newton's method is the key to solving these problems.

Finally, you'll study optimization. In calculus, optimization is a method for determining the largest or smallest value of a function. Let's say that you want to know the largest possible area you can enclose with a fence based on the amount of fencing materials you have. This is where derivatives can save the day. We promised that calculus can be helpful in the real world.

Video Objectives
Linearization of Functions Learn how to define the linearization of a function and use linearization to estimate travel time.
How to Estimate Function Values Using Linearization Explore how to estimate the value of a function using linearization.
What Is Newton's Method? See an explanation and an example of Newton's method at work.
How to Use Newton's Method to Find Roots of Equations Learn to use Newton's Method instead of a calculator to find the root of any equation
Optimization and Differentiation Learn what optimization means from a mathematical standpoint and how it relates to differentiation.
Optimizing Simple Systems Discover how to use a handy five-step formula to tackle to simple optimization problems.
Optimizing Complex SystemsLearn a five-step process to solve complex optimization problems.

7 Lessons in Chapter 10: Applications of Derivatives
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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