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Higher Order Derivatives: MATH 171 Problems 4-6 thumbnail

Higher Order Derivatives: MATH 171 Problems 4-6

Finding a formula for a higher order derivative and a formula for the second derivative of a product

Chain RuleDerivativeFactorialHigher DerivativeInductionnth DerivativePower RuleProduct RuleRational FunctionSecond Derivative
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Studying the Shape of Curves: MATH 171 Problems 1-3 thumbnail

Studying the Shape of Curves: MATH 171 Problems 1-3

What the derivatives of a function tell us about the shape of its graph

Concave DownConcave UpDecreasingDecreasing FunctionDerivativeDiscontinuous FunctionFirst DerivativeGraphGraph of DerivativeIncreasingIncreasing FunctionLineRelative MaximumRelative MinimumSecond Derivative
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Optimization: MATH 171 Problems 1-3 thumbnail

Optimization: MATH 171 Problems 1-3

Optimizing values in word problems

Absolute MaximumAbsolute MinimumAreaCritical ValueDerivativeDistance from a Point to a LineFirst Derivative TestGraphIncreasing FunctionLineMaximizeMinimizeRelative MaximumRelative MinimumSecond Derivative TestVolumeWord Problems
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Higher Derivatives Example 1 thumbnail

Higher Derivatives Example 1

The definition of higher derivatives and solving an example

DerivativeFirst DerivativeHigher DerivativeMATH 147Power FunctionPower RuleSecond Derivative
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Higher Derivatives Example 2 thumbnail

Higher Derivatives Example 2

Using derivatives to find the velocity and acceleration functions from the position function

AccelerationChain RuleDerivativeFirst DerivativeHigher DerivativeMATH 147PositionPower FunctionPower RuleSecond DerivativeSquare RootVelocity
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Optimization Example 2 thumbnail

Optimization Example 2

Using the second derivative to find the maximum rate of change in a word problem

Chain RuleCritical NumberDerivativeExponential FunctionFirst DerivativeLogarithmMATH 147MaximizeOptimizationProperties of ExponentsSecond Derivative
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Review for the Common Exam: MATH 151 Exam 2 Review Problems 16-20 thumbnail

Review for the Common Exam: MATH 151 Exam 2 Review Problems 16-20

Derivatives of parametric equations and tangent lines

AccelerationAngleChain RuleCosineDerivativeParallelParametric EquationsPositionProduct RuleSecond DerivativeSineSlopeTangent LineVectorVelocity
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Review for the Common Exam: MATH 151 Exam 3 Review Problems 1-7 thumbnail

Review for the Common Exam: MATH 151 Exam 3 Review Problems 1-7

Derivatives of exponential functions and the exponential model

Absolute ValueChain RuleCosineDerivativeExponential DecayExponential FunctionExponential GrowthExponential ModelFirst DerivativeHalf-LifeImplicit DifferentiationLogarithmProduct RuleRate of ChangeSecond DerivativeTangent
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Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19 thumbnail

Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19

Mean Value Theorem and using derivatives to find the shape of curves

Absolute MaximumAbsolute MinimumChain RuleConcave DownConcave UpConcavityContinuous FunctionCritical NumberCritical ValueDecreasingDerivativeExponential FunctionFirst DerivativeGraphIncreasingInflection PointLocal MaximumLocal MinimumLogarithmMean Value TheoremPolynomialProduct RuleQuotient RuleRational FunctionSecond DerivativeSine
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