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Continuity: MATH 171 Problems 6 & 7 thumbnail

Continuity: MATH 171 Problems 6 & 7

Proving a piecewise function and a polynomial are continuous

ContinuousContinuous at x=aDiscontinuityDiscontinuous FunctionGraphLimitLimit PropertiesPiecewise FunctionPolynomialRational Function
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Continuity: MATH 171 Problems 8 & 9 thumbnail

Continuity: MATH 171 Problems 8 & 9

Proving a product of continuous functions is continuous and using the Intermediate Value Theorem

ContinuousContinuous at x=aContinuous FunctionIntermediate Value TheoremLimitLimit PropertiesPolynomial
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Differentiation Formulas: MATH 171 Problems 6 & 7 thumbnail

Differentiation Formulas: MATH 171 Problems 6 & 7

Proving the Product Rule and the rule for the derivative of a difference of functions

Continuous FunctionDerivativeDerivative RulesDifference QuotientLimitLimit Definition of the DerivativeProduct Rule
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Trigonometry Derivatives and the Chain Rule: MATH 171 Problems 1-3 thumbnail

Trigonometry Derivatives and the Chain Rule: MATH 171 Problems 1-3

Proving the derivatives of trigonometric functions and that sine is continuous

ContinuousContinuous at x=aContinuous FunctionCosineDerivativeDifference QuotientLimitLimit Definition of the DerivativeQuotient RuleSecantSineTangentTrigonometry
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Absolute Extrema: MATH 171 Problems 4 & 5 thumbnail

Absolute Extrema: MATH 171 Problems 4 & 5

Proving Fermat's Theorem and graphing local and absolute extrema

Absolute MaximumAbsolute MinimumCritical ValueDerivativeDifference QuotientDiscontinuous FunctionExtreme Value TheoremLimitLimit from the LeftLocal MaximumLocal MinimumOne-Sided LimitRelative MaximumRelative Minimum
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Mean Value Theorem: MATH 171 Problems 6-8 thumbnail

Mean Value Theorem: MATH 171 Problems 6-8

Using the Mean Value Theorem to prove facts about functions

Continuous FunctionDecreasing FunctionDerivativeDifference QuotientIntermediate Value TheoremMean Value TheoremPolynomial
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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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L'Hospital's Rule: MATH 171 Problems 7-9 thumbnail

L'Hospital's Rule: MATH 171 Problems 7-9

Proving L'Hospital's Rule and using it to evaluate limits

Chain RuleContinuousContinuous at x=aDerivativeDifferentiableeGraphIndeterminate FormL'Hopital's RuleLimitLimit Involving InfinityLogarithm
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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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