MiddelværdisætningenMean value theorem example: polynomialMean value theorem example: square root functionJustification with the mean value theorem: tableJustification with the mean value theorem: equationEstablishing differentiability for MVTMean value theorem applicationMean value theorem review

EkstremværdisætningenCritical points introductionFinding critical points

Finding decreasing interval given the functionFinding increasing interval given the derivativeIncreasing & decreasing intervals review

Introduction to minimum and maximum pointsFinding relative extrema (first derivative test)Worked example: finding relative extremaAnalyzing mistakes when finding extrema (example 1)Analyzing mistakes when finding extrema (example 2)Finding relative extrema (first derivative test)Relative minima & maxima review

Finding absolute extrema on a closed intervalAbsolute minima & maxima (entire domain)Absolute minima & maxima review

Concavity introductionAnalyzing concavity (graphical)Inflection points introductionInflection points (graphical)

Analyzing concavity (algebraic)Inflection points (algebraic)Mistakes when finding inflection points: second derivative undefinedMistakes when finding inflection points: not checking candidatesAnalyzing the second derivative to find inflection pointsConcavity reviewInflection points review

Anden afledte test

Curve sketching with calculus: polynomialCurve sketching with calculus: logarithmAnalyzing a function with its derivative

Calculus based justification for function increasingJustification using first derivativeJustification using first derivativeInflection points from graphs of function & derivativesJustification using second derivative: inflection pointJustification using second derivative: maximum pointJustification using second derivativeConnecting f, f', and f'' graphicallyConnecting f, f', and f'' graphically (another example)

Optimization: sum of squaresOptimization: box volume (Part 1)Optimization: box volume (Part 2)Optimization: profitOptimization: cost of materialsOptimization: area of triangle & square (Part 1)Optimization: area of triangle & square (Part 2)Optimization problem: extreme normaline to y=x²Motion problems: finding the maximum acceleration

Horizontal tangent to implicit curve