Calculus 1: Definition of the Derivative
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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
Find the derivative of the following function using the limit definition of derivative,
##f(x) = 8x + 4 ##
##f(x) = 8x + 4 ##
Use the definition of derivatives to find the derivative of the following function,
##f(x) = \sqrt{x - 1} ##
##f(x) = \sqrt{x - 1} ##
Find the slope of the tangent line to
##f(x) = \sqrt{x} ##
when x = 1
##f(x) = \sqrt{x} ##
when x = 1
Find the slope of the tangent line to
##f(x) = \frac{1}{x} ##
when x = 4
##f(x) = \frac{1}{x} ##
when x = 4
Use the definition of the derivative to find ##f\prime(x)## if
##f(x) = \frac{2}{3 - 5x} ##
##f(x) = \frac{2}{3 - 5x} ##
Use the limit definition of the derivative to find the equation of the tangent line for the graph of
##y = x^2 - 3x + 2 ## at (2, 0)
##y = x^2 - 3x + 2 ## at (2, 0)
Use the limit definition of the derivative to find the equation of the normal line to the graph of
##f(x) = \frac{1}{\sqrt{4 - x}} ## at ##x = 3##
##f(x) = \frac{1}{\sqrt{4 - x}} ## at ##x = 3##
Use the limit definition of the derivative to find all points on the graph of
##f(x) = 4x^3 - 12x^2 + 9x ##
where the tangent lines to the graph have slope zero.
##f(x) = 4x^3 - 12x^2 + 9x ##
where the tangent lines to the graph have slope zero.