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Master Critical Numbers: Find Maximum and Minimum Values

Calculus 1: Master Core Concepts & Applications

Limits

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Intermediate value theorem

Proving the Existence of Real Roots Using IVT

Intermediate Value Theorem

Application of Intermediate Value Theorem

Proving the Existence of a Real Root Using IVT

Finding limits from graphs  

Continuity

Discontinuities of Rational Functions (denominator=0)

Finding limits algebraically - direct substitution 

Finding limits algebraically - when direct substitution is not possible

Infinite limits - vertical asymptotes  

Limits at infinity - horizontal asymptotes

Limit Evaluation

Limits at Infinity of Exponential Functions

Squeeze theorem

Quadratic Function with Integer Vertex

Limit laws

Evaluating Limits of Functions

limit laws

Evaluating Limits with specific limits given

Introduction to Calculus - Limits 

Differentiation

Estimating derivatives from a table

Slope and equation of tangent line

Chain rule

Chain Rule

Differentiation of Trigonometric Function

Differentiate Radical Functions with Chain Rule

Differentiate: Trigonometric Functions

Chain rule: Differentiate Trigonometric Functions

Differentiation of Exponential Function

Differentiation of Exponential Functions

Differentiation: Chain Rule with Logarithmic Functions

Differentiation of Logarithmic Function

Product rule

Quotient rule

Differentiation using Quotient Rule

Differentiation using Chain Rule and Quotient Rule

Derivative of inverse trigonometric functions

Definition of derivative  

Definition of Derivative

Definition of derivative

Derivative using Definition

Vertical Tangent Line of a Function

Applications to definition of derivative

Power rule

Power Rule

Application of the Power Rule

Power rule application

Applying Power Rule

Power Rule with Negative Exponents

Power rule with rational exponents

Power rule and rational exponents

Derivative of trigonometric functions  

Derivative of Trigonometric Functions

Derivative of Composite Trig Functions

Derivative of exponential functions

Derivative of Exponential Functions

Differentiation of Composite Functions

Derivative of power and exponential functions

Derivative of logarithmic functions

Derivative of log with arbitrary base

Derivative of Natural Logarithm Functions

Derivative of Logarithmic Functions

Implicit differentiation

Higher order derivatives

Higher Order Derivatives

First and second derivatives

First and Second Derivatives

Second derivatives with implicit differentiation

Implicit Differentiation

Higher Order Derivatives with Repeating Patterns

Applications of differentiation

Mean value theorem 

Mean Value Theorem

Mean value theorem

Mean Value Theorem Application

Critical number & maximum and minimum values

Critical Number & Maximum and Minimum Values

Linear approximation

Use of Linear Approximations in Estimating Square Roots

Linearization of Radical Functions

Linearization of Polynomial Functions

Linearization of Rational Functions

Linearization of Exponential Functions

Linearization of Logarithmic Functions

Linear Approximation of Trigonometric Functions

Optimization

Position velocity acceleration

Velocity of a Particle

Total Distance Traveled by a Particle

Comparative Analysis of Particle's Velocity and Acceleration

Curve sketching

Related rates

l'Hospital's rule

l'Hopital's rule

l'Hospital's Rule

Evaluating the limit using L'Hospital's Rule

l"Hospital"s rule

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Calculus 1

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<h2>What is Calculus?</h2>
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<h2>Is calculus hard?</h2>
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Intro

Ex. 2

Ex 3.

Visual intuition behind the first derivative test

Ex .4.

Ex. 5.

Visual intuition for the closed interval method

Ex. 6.

Finding absolute extrema on [-1/2, 1/2] using the closed interval method

Intro to local extrema, critical points, and critical numbers

Finding absolute maximum and minimum values on a graph

Finding absolute extrema on a closed interval using a graph

Finding critical numbers of a cube root function

Finding critical numbers of a function with fractional exponents

Finding critical numbers of a degree-5 polynomial using synthetic division

Finding intervals of increase and decrease using the first derivative

Identifying local max and min using the first derivative test

Sketching the graph using critical numbers and local extrema

Why a degree-5 polynomial has no absolute max or min

Another powerful usage of differential calculus is optimization, for example, finding the number of products needed to be sold at a store to maximize its monthly revenue or to minimize its monthly costs. In this section, we will link the application of differential calculus with finding the local extrema, the maxima and minima, of a function. 

Critical number and maximum and minimum values

Critical number, maximum and minimum values

Critical Numbers: The Key to Maximum and Minimum Values

What You'll Learn

Identify critical numbers by finding where the derivative equals zero or is undefined

Apply the first derivative test to determine local maxima and minima

Distinguish between local extrema and absolute extrema on different intervals

Use the closed interval method to find absolute maximum and minimum values

Analyze increasing and decreasing intervals using the sign of the derivative

What You'll Practice

Finding critical numbers by solving derivative equations and factoring polynomials

Testing intervals to determine where functions increase or decrease

Evaluating functions at critical numbers and endpoints to locate absolute extrema

Sketching graphs using critical points and interval analysis

Why This Matters

This Unit Includes

13 Video lessons

Practice exercises

Learning resources

Skills

Critical Numbers

Derivatives

Local Extrema

Absolute Extrema

First Derivative Test

Closed Interval Method

Optimization

Increasing/Decreasing Functions