# Finding Extreme Points

In the lesson on understanding limits, we learned how to use limits to calculate the point a function approaches when the input value approaches a specific value. We applied this technique to calculate the slope of the tangent line at a specific point on a nonlinear function. As mentioned in the first lesson in this Calculus for Machine Learning course, we’re interested in determining the highest point on this curve.

If you’ve ever hiked a mountain before, you’ll be familiar with how the trail slopes up until you reach the peak. Once you’re at the peak, however, all of the paths back down slopes downwards. Understanding how the slope varies throughout a curve provides a useful lens for determining the maximum point on a curve.

In this lesson, you will learn a critical concept of calculus known as the derivative. A function’s derivative can tell us the slope of the tangent line for any value along the function. You’ll learn how to use a process known as differentiation to find a function’s derivative. In addition, you’ll learn other important calculus concepts known as critical points, extreme values, the power rule as well the linearity of differentiation. All of these concepts are important for understanding what’s happening in various machine learning algorithms.

As you work through each concept, you’ll get to apply what you’ve learned from within your browser so that there’s no need to use your own machine to do the exercises. The Python environment inside of this course includes answer checking so you can ensure that you’ve fully mastered each concept before learning the next concept.

## Objectives

- Learn how to find extreme points in a nonlinear function.
- Learn how to compute the derivative of a nonlinear function.

## Lesson Outline

- Recap
- Introduction To Derivatives
- Differentiation
- Critical Points
- Extreme Values
- Power Rule
- Linearity Of Differentiation
- Practicing Finding Extreme Values
- Next Steps
- Takeaways

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