Analyzing functions videos

Mean value theorem

Mean value theorem example: polynomial

Justification with the mean value theorem: equation

Mean value theorem example: square root function

Justification with the mean value theorem: table

Mean value theorem application

Extreme value theorem

Critical points introduction

Finding critical points

Finding increasing interval given the derivative

Finding decreasing interval given the function

Introduction to minimum and maximum points

Worked example: finding relative extrema

Finding relative extrema (first derivative test)

Analyzing mistakes when finding extrema (example 1)

Analyzing mistakes when finding extrema (example 2)

Finding absolute extrema on a closed interval

Absolute minima & maxima (entire domain)

Concavity introduction

Inflection points introduction

Analyzing concavity (graphical)

Inflection points (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

Analyzing a function with its derivative

Curve sketching with calculus: logarithm

Justification using first derivative

Calculus-based justification for function increasing

Inflection points from graphs of function & derivatives

Justification using second derivative: inflection point

Connecting f, f', and f'' graphically

Justification using second derivative: maximum point

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

Optimization: box volume (Part 2)

Optimization: profit

Optimization: sum of squares

Optimization: box volume (Part 1)

Optimization: cost of materials

Optimization: area of triangle & square (Part 1)

Optimization: area of triangle & square (Part 2)

Optimization problem: extreme normaline to y=x²

Motion problems: finding the maximum acceleration

Horizontal tangent to implicit curve