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
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
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
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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.