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Calculus 1: Graphing and Critical Points

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All Calculus 1LimitsDefinition of the DerivativeProduct and Quotient RulePower Rule and Basic DerivativesDerivatives of Trig FunctionsExponential and Logarithmic FunctionsChain RuleInverse and Hyperbolic Trig DerivativesImplicit DifferentiationRelated Rates ProblemsLogarithmic DifferentiationGraphing and Critical PointsOptimization ProblemsIndeterminate Forms and l'Hospital's RuleLinear Approximation and DifferentialsNewton Raphson MethodIndefinite IntegralsU SubstitutionDefinite Integrals and Fundamental TheoremApplications of Integration
Critical Points and Local Maximum

y=x2/3(2−x)y = x^{2/3}(2-x)

Find: A. The critical values of x? B. The x coordinate of the local maximum

Graphing and Critical PointsMediumVideo
Concave Up Concave Down

Find the inflection points for the following function and determine intervals of concave up and concave down on the graph

f(x)=ln⁡(1−ln⁡(x))f(x) = \ln{(1 - \ln{(x)})}

Graphing and Critical PointsMediumVideo
Inflection Point Calculus

Find the inflection points and intervals of concavity for the following function

y=x2+1x2y = \frac{x^2 + 1}{x^2}

Graphing and Critical PointsMediumVideoNeeds Solution