Krista King Math
Linear Approximation
What's in a line? Viewers of an illuminating video learn how to determine the linear approximation of a quadratic function at a specific value. The narrator of the video works through an example problem on the concept.
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Linearization of a Function at a Point
Sometimes the only important thing about function is how it behaves around a single point. Pupils learn about the linearization of a function at a point by watching a video. They see an example of the topic using a trigonometric function.
Krista King Math
Optimization - Calculus
Get the maximum possible benefit from an optimal video. Scholars first review how to find critical points and how to test for local and global maxima and minima. They then apply these skills to a geometric optimization problem.
Krista King Math
How to Find Critical Points
It's critical to find the critical points. Pupils learn how to identify the critical points of a function. By looking at an example, they see how to determine the derivative function, find the critical numbers, and test to determine...
Krista King Math
How to Use the Second Derivative Test
Two derivative tests are better than one. By watching an informative video, learners discover how to apply the second derivative test. They see that classifying a critical point as a local maximum or minimum requires substituting into...
Krista King Math
Integrals - Calculus
Introduce the opposite of differentiation. Pupils learn the basic definition of integration and how to integrate a polynomial. The video shows learners how the integral is the opposite of the derivative. Individuals see how to confirm...
Krista King Math
U-Substitution in Definite Integrals
The process definitely works two ways. Viewers watch as the video shows how to use u-substitution to evaluate a definite integral. The presenter uses two different methods to evaluate the integral. One method substitutes the expression...
Krista King Math
U-Substitution
U need to substitute to make it easier to integrate. A short video shows learners how to use U-substitution to find the integral of a binomial raised to a power. In the examples, scholars do not have to determine the quantity to...
Krista King Math
Solving Integrals
Find out how to integrate when simple integration is not enough. Learners view examples of complex integrals that require a different approach to solve. The video presents three methods to solve integrals: U-substitution, integration by...
Krista King Math
Properties of integrals
Use properties properly to evaluate a definite integral. Pupils watch an informative video to see how three different properties of integrals help with the evaluation of a definite integral. The presenter uses the properties to separate...
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Indefinite Integrals
Generally, there's a good way to find the general form of the integral of a polynomial expression. Pupils view the determination of an indefinite integral of a simple polynomial function. The presenter takes the integral one term at a...
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Fundamental Theorem of Calculus Part 2
Use the Fundamental Theorem, not just look at it. Learners watch as the video walks viewers through finding the definite integral of a trigonometric function. The presenter provides helpful suggestions as she evaluates the example...
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Part 1 of the Dreaded Fundamental Theorem of Calculus!
Use the Fundamental Theorem of Calculus to find a derivative. With an example, pupils observe how being to derive a formula to help determine the derivative of any given integral. The video derives the formula using the first part of the...
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Dimensions That Maximize the Area of the Rectangle
Opt to learn about optimization. Young mathematicians view an educational video that posits the question: For a given perimeter, what are the dimensions that maximum the area of a rectangle? With the use of optimization skills, they...
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Maxima and Minima On a Closed Interval
Close the chapter on extrema on a closed interval. Watching an informative video provides scholars with an opportunity to learn about extrema. Specifically, they see how to find the global maxima and minima on a closed interval by first...
Krista King Math
All About Graph Sketching!!
There's nothing sketchy about a helpful graphing resource. An informative video shows how to sketch graphs of functions. Scholars first apply derivatives to determine increasing/decreasing behavior, concavity, and asymptotes. They then...
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How to Find Slant Asymptotes
Learn about slant asymptotes directly—not obliquely. Viewers of a short video discover how to determine a slant or oblique asymptote for a rational function. They see how to apply polynomial division to achieve this goal.
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How to Find Horizontal Asymptotes
Is a vertical asymptote required to find the horizontal counterpart? By watching a video, scholars learn how to determine the horizontal asymptote of the graph of a rational function. They recognize that the degrees of the leading terms...
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How to Find Vertical Asymptotes!!
Ascertain the asymptotes. An informative video describes how to algebraically determine the locations of vertical asymptotes for the graphs of rational functions. Scholars see that they need to set the denominator equal to zero and solve...
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First Derivative Test to Find the Max and Min
It only takes a minimum amount of effort to understand optimization. Pupils watch an illuminating video to learn about applications of the first derivative test. They see how to find critical points and then check to see whether each...
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Inflection Points and Concavity
Confused about concavity? Here's the perfect video. Young mathematicians watch a video that explains the process of using the second derivative to determine inflection points and the concavity of a function. An example reinforces the...
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Where Is the Function Increasing and Decreasing?!
Increase understanding of increasing and decreasing behavior. Viewers of an instructional video learn how to identify intervals where a function is increasing and decreasing using critical points and the first derivative test. They watch...
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Estimate the Root with Linear Approximation
Root for those learning about roots. An installment of an extensive playlist covering derivatives focuses on using linear approximations to estimate roots. The example problem shows how to find the fourth root of 15 without a calculator.
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Equation of the Normal Line at a Point
Is it normal to find a perpendicular line to the tangent line? The short video provides a problem to find the equation of the normal line to a function. Beginning with an explanation of the normal line, the 27th installment in a 31-part...