converting derivative graphs to functions 42 videos
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The Derivative Function
Calculus The Derivative
How to define the derivative function f'(x).
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Derivatives of Power Functions
Calculus The Derivative
How to determine the derivative of a power function.
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Derivatives of Linear Functions
Calculus The Derivative
How to determine the derivative of a linear function.
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Derivatives of Polynomial Functions
Calculus The Derivative
How to compute the derivative of a polynomial function using two properties of the derivative.
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Derivatives of Exponential Functions
Calculus The Derivative
How to use the definition of the derivative to find a derivative formula for exponential functions.
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Derivatives of Logarithmic Functions
Calculus The Derivative
How to infer the derivative of the natural log function using a calculator investigation.
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The Definition of the Derivative
Calculus The Derivative
How to define the derivative of a function at a point x=a.
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Derivative Notation
Calculus The Derivative
How to recognize and use Newton's and Leibniz's notation for the derivative.
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Continuous Functions
Calculus Limits and Continuity
How to determine whether a function f(x) is continuous everywhere on its domain.
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The Product Rule
Calculus Techniques of Differentiation
How to differentiate a product of two functions.
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Antidifferentiation
Calculus Antiderivatives and Differential Equations
How to find an antiderivative of a function.
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Curve Sketching with Derivatives
Calculus Applications of the Derivative
How to evaluate the limit of a function using continuity.
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Average Value of a Function
Calculus The Definite Integral
How to find the average value of a function over an interval [a,b].
average value antidifferentiation limits of integration functions area under a curve -
Optimization Using the First Derivative Test
Calculus Applications of the Derivative
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.
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The Second Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to show that polynomial functions are continuous functions.
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Chain Rule: The General Logarithm Rule
Calculus Techniques of Differentiation
How to differentiate a composite function when the outside function is the natural logarithm.
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Economics: Marginal Cost & Revenue
Calculus Applications of the Derivative
How to interpret the derivatives of the cost and revenue functions as marginal cost and marginal revenue.
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The Chain Rule
Calculus Techniques of Differentiation
How to differentiate a composite function.
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Chain Rule: The General Power Rule
Calculus Techniques of Differentiation
How to differentiate a composite function when the outside function is a power function.
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Limits: A Graphical Approach
Calculus Limits and Continuity
How to determine one-sided and two-sided limits from the graph of a function.
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