Analyzing functions videos

Mean value theorem

Mean value theorem example: polynomial

Mean value theorem example: square root function

Mean value theorem application

Justification with the mean value theorem: table

Justification with the mean value theorem: equation

Extreme value theorem

Critical points introduction

Finding critical points

Finding decreasing interval given the function

Finding increasing interval given the derivative

Finding relative extrema (first derivative test)

Introduction to minimum and maximum points

Worked example: finding relative extrema

Analyzing mistakes when finding extrema (example 1)

Analyzing mistakes when finding extrema (example 2)

Absolute minima & maxima (entire domain)

Finding absolute extrema on a closed interval

Concavity introduction

Inflection points introduction

Inflection points (graphical)

Analyzing concavity (graphical)

Analyzing concavity (algebraic)

Mistakes when finding inflection points: not checking candidates

Mistakes when finding inflection points: second derivative undefined

Inflection points (algebraic)

Second derivative test

Curve sketching with calculus: polynomial

Curve sketching with calculus: logarithm

Analyzing a function with its derivative

Calculus-based justification for function increasing

Justification using first derivative

Connecting f, f', and f'' graphically

Justification using second derivative: inflection point

Inflection points from graphs of function & derivatives

Justification using second derivative: maximum point

Connecting f, f', and f'' graphically (another example)

Optimization: box volume (Part 1)

Optimization: sum of squares

Optimization: box volume (Part 2)

Optimization: cost of materials

Optimization: profit

Optimization: area of triangle & square (Part 2)

Optimization: area of triangle & square (Part 1)

Motion problems: finding the maximum acceleration

Optimization problem: extreme normaline to y=x²

Horizontal tangent to implicit curve