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Analyzing functions

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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
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EkstremværdisætningenCritical points introductionFinding critical points
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Finding decreasing interval given the functionFinding increasing interval given the derivativeIncreasing & decreasing intervals review
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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
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Finding absolute extrema on a closed intervalAbsolute minima & maxima (entire domain)Absolute minima & maxima review
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Concavity introductionAnalyzing concavity (graphical)Inflection points introductionInflection points (graphical)
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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
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Anden afledte test
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Curve sketching with calculus: polynomialCurve sketching with calculus: logarithmAnalyzing a function with its derivative
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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)
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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
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Horizontal tangent to implicit curve
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Om dette emne

The first and the second derivative of a function can be used to obtain a lot of information about the behavior of that function. For example, the first derivative tells us where a function increases or decreases and where it has maximum or minimum points; the second derivative tells us where a function is concave up or down and where it has inflection points.