Finding Critical Numbers

This calculus video tutorial explains how to find the critical numbers of a function. These include trig functions, absolute value functions, rational functions, fractions, square roots and more. To find the critical number, find the first derivative of the function, set it equal to zero, and solve for x. If you have a fraction as a derivative, set the numerator and denominator of the fraction equal to zero and solve. Critical numbers occur when f'(c) = 0 or when f'(c) does not exist as in the case of a cusp. This calculus video contains plenty of examples and practice problems.

Introduction to Limits:

Derivatives - Fast Review:

Introduction to Related Rates:

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Extreme Value Theorem:

Finding Critical Numbers:

Local Maximum & Minimum:

Absolute Extrema:

Rolle's Theorem:

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Mean Value Theorem:

Increasing and Decreasing Functions:

First Derivative Test:

Concavity & Inflection Points:

Second Derivative Test:

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L'Hopital's Rule:

Curve Sketching With Derivatives:

Newton's Method:

Optimization Problems:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

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Another interesting way to solve the absolute value problem is to realize that |x| = sqrt(x^2), and finding the derivative that way. Derivative of |x| would be |x|/x, then just use the chain rule. I thought that was an interesting alternate solution.

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So whenever you are finding the critical number of a fraction/ rational function you set both the numerator and denominator equal to zero?

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2:04 "set the numerator equal to x" - don't you mean equal to 0?

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