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Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3 thumbnail

Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3

Proving facts about the derivatives of vector functions including the product rule

CosineDerivativeDifference QuotientDot ProductGraphLimitLimit Definition of the DerivativeOrthogonalProduct RuleSineSum RuleTrigonometryVectorVector DerivativeVector Function
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Derivatives and Rates of Change: MATH 171 Problems 1-3 thumbnail

Derivatives and Rates of Change: MATH 171 Problems 1-3

Using the limit definition to find derivatives of functions and vector functions

DerivativeDifference QuotientGraphLimitLimit Definition of the DerivativeLineRational FunctionSlopeSquare RootTangent LineVectorVector DerivativeVector Function
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Differentiation Formulas: MATH 171 Problems 4 & 5 thumbnail

Differentiation Formulas: MATH 171 Problems 4 & 5

Using the limit definition to find a derivative and proving the power rule

Absolute ValueDerivativeDerivative RulesDifference QuotientLimit Definition of the DerivativePiecewise FunctionPower FunctionPower Rule
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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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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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MLC WIR 20B M151 week10 #6c thumbnail

MLC WIR 20B M151 week10 #6c

Using L'Hospital's Rule to evaluate a limit representing a derivative at a point

DerivativeDifference QuotientIndeterminate FormL'Hopital's RuleLimitLimit Definition of the DerivativeMATH 151Rational Function
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