Analyzing functions
17 videos
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Calculus 1 - Analyzing Functions with Calculus: What You Need to Know
Learn how calculus uses derivatives to find optimal values, critical points, and function behavior. Discover how to maximize profit and solve real-world optimization problems.
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Calculus 1 - The Mean Value Theorem
An introduction to the Mean Value Theorem in calculus, explaining how instantaneous rate of change must equal average rate of change at some point in a continuous function.
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Calculus 1 - Applying the Mean Value Theorem
Learn how to apply the Mean Value Theorem by finding where instantaneous rate equals average rate. Includes step-by-step example with derivatives and solving for c.
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Calculus 1 - Critical Points of a Function
Learn what critical points are in calculus, where they occur when derivatives equal zero or don't exist, and how they relate to peaks and valleys on function graphs.
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Calculus 1 - Finding Increasing and Decreasing Intervals
Learn how to use the first derivative to find where a function is increasing or decreasing by analyzing the sign of the derivative through a worked example.
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Calculus 1 - The First Derivative Test for Relative Extrema
Explains the first derivative test for identifying relative maxima and minima by analyzing sign changes of the derivative at critical points.
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Calculus 1 - Finding Relative Extrema: Step-by-Step
Learn how to find relative extrema using the first derivative test by analyzing critical points and sign changes to identify maxima and minima without graphing.
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Calculus 1 - Absolute Extrema on Closed Intervals
Learn how to find absolute maximum and minimum values using the Extreme Value Theorem by evaluating endpoints and critical points on a closed interval.
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Calculus 1 - Absolute Extrema Over the Entire Domain
Learn how to find absolute extrema of functions on infinite domains by finding critical points, checking end behavior, and comparing values to determine absolute max or min.
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Calculus 1 - Concavity and the Second Derivative
This video explains concavity in calculus using the second derivative. It shows how positive values create concave up curves and negative values create concave down curves.
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Calculus 1 - Inflection Points
Learn what inflection points are, how they relate to concavity changes, and why the second derivative's sign change is crucial for identifying them.
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Calculus 1 - Finding Inflection Points Algebraically
Learn how to find inflection points algebraically using the second derivative and verify them by checking for sign changes at candidate points.
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Calculus 1 - The Second Derivative Test
Learn how the second derivative test determines if a critical point is a local minimum, maximum, or inconclusive by analyzing concavity.
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Calculus 1 - Connecting f, f', and f'' Graphically
Learn to identify f, f', and f'' from mystery curves by matching zeros with peaks/valleys and inflection points. Master this key calculus connection for AP exams.
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Calculus 1 - Calculus-Based Justifications on the AP Exam
Learn how to write calculus-based justifications for AP exams by naming derivatives, stating their signs, and drawing conclusions about function behavior.
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Calculus 1 - Setting Up Optimization Problems
Learn the three-step process for solving optimization problems in calculus: identify what to optimize, write an equation, and use constraints to reduce to one variable.
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Calculus 1 - Solving an Optimization Problem
Learn how to use calculus to maximize the product of two numbers that sum to 50. Demonstrates derivatives, critical points, and the second derivative test.