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Analyzing functions with calculus

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Introduction to minimum and maximum pointsIdentifying relative minimum and maximum valuesCritical 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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Finding relative extrema (first derivative test)Analyzing a function with its derivativeWorked example: finding relative extremaRelative minima & maxima review
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Extreme value theoremFinding absolute extrema on a closed intervalAbsolute minima & maxima (entire domain)Absolute minima & maxima review
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Concavity introductionAnalyzing concavity (graphical)Analyzing concavity (algebraic)Second derivative testConcavity review
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Inflection points introductionInflection points (graphical)Worked example: Inflection points from first derivativeInflection points (algebraic)Inflection points review
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Curve sketching with calculus: polynomialCurve sketching with calculus: logarithm
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About this unit

Let's put all of our differentiation abilities to use, by analyzing the graphs of various functions. As you will see, the derivative and the second derivative of a function can tell us a lot about the function's graph.