converting derivative graphs to functions 42 videos

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.

Average Value of a Function
Calculus The Definite Integral
How to find the average value of a function over an interval [a,b].
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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.

The Second Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to show that polynomial functions are continuous functions.

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 onesided and twosided limits from the graph of a function.
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