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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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Fundamental Theorem of Calculus: MATH 171 Problems 1-3 thumbnail

Fundamental Theorem of Calculus: MATH 171 Problems 1-3

Proving and then applying the Fundamental Theorem of Calculus

AntiderivativeAntiderivative of a FunctionConcave DownConcave UpContinuousDerivativeDifference QuotientDifferentiableExtreme Value TheoremFundamental Theorem of CalculusGraphGraph of AntiderivativeGraph of DerivativeIncreasingIntegralLimitSqueeze (or Sandwich) Theorem
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Monotone Sequence Theorem: MATH 172 Problems 6-8 thumbnail

Monotone Sequence Theorem: MATH 172 Problems 6-8

Using the Monotone Sequence Theorem and induction to show a sequence converges

Bounded SequenceConvergent SequenceDecreasingIncreasingInductionL'Hopital's RuleLimitMonotone Sequence Theorem
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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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MLC WIR 20B M151 week9 #1 thumbnail

MLC WIR 20B M151 week9 #1

Determining the properties of a function from the graph of its derivative

Concave DownConcave UpDecreasingDerivativeFirst DerivativeGraphIncreasingInflection PointLocal MaximumLocal MinimumMATH 151Relative MaximumRelative Minimum
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MLC WIR 20B M151 week9 #2 thumbnail

MLC WIR 20B M151 week9 #2

Using the derivative to determine where a function is increasing and decreasing

Absolute MaximumAbsolute MinimumCritical ValueDerivativeFirst DerivativeMATH 151
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MLC WIR 20B M151 week9 #3 thumbnail

MLC WIR 20B M151 week9 #3

Finding the absolute maximum and minimum values of a function on a closed interval

Critical ValueDecreasingDerivativeFirst DerivativeIncreasingMATH 151
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MLC WIR 20B M151 week9 #4 thumbnail

MLC WIR 20B M151 week9 #4

Finding the intervals where a function is increasing and decreasing and its local maximums and minimums

Critical ValueDecreasingDerivativeFirst DerivativeIncreasingLocal MaximumLocal MinimumMATH 151Relative MaximumRelative Minimum
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