polynomial functions 34 videos

Derivatives of Polynomial Functions
Calculus The Derivative
How to compute the derivative of a polynomial function using two properties of the derivative.
the constant multiple rule the sum rule of derivatives polynomial functions derivative 
Continuous Functions
Calculus Limits and Continuity
How to determine whether a function f(x) is continuous everywhere on its domain.
limits definition of continuous function domain of a function power functions exponential functions logarithmic functions 
The Derivative Function
Calculus The Derivative
How to define the derivative function f'(x).
derivative limits the derivative function 
Derivatives of Linear Functions
Calculus The Derivative
How to determine the derivative of a linear function.
linear functions derivative slope 
Derivatives of Power Functions
Calculus The Derivative
How to determine the derivative of a power function.
power functions derivative derivative formula 
Derivatives of Exponential Functions
Calculus The Derivative
How to use the definition of the derivative to find a derivative formula for exponential functions.
limits derivative definition of the derivative difference quotient exponential functions natural logarithm 
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 
Evaluating Limits Algebraically, Part 2
Calculus Limits and Continuity
How to evaluate the limit of a function at points where it is not continuous.
limits definition of continuous function domain of a function rational functions factoring polynomials holes 
The Chain Rule
Calculus Techniques of Differentiation
How to differentiate a composite function.
composite function composition inside function outside function differentiation 
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 Power Rule
Calculus Techniques of Differentiation
How to differentiate a composite function when the outside function is a power function.
chain rule composite functions power functions power rule differentiation 
Chain Rule: The General Exponential Rule
Calculus Techniques of Differentiation
How to differentiate a composite function when the outside function is exponential.
chain rule composite functions composition exponential functions 
Tricky Substitutions Involving Radicals
Calculus Antiderivatives and Differential Equations
How to antidifferentiate functions with radicals.
substitution antidifferentiation radical functions 
Evaluating Limits Algebraically, Part 1
Calculus Limits and Continuity
How to evaluate the limit of a function using continuity.
limits definition of continuous function domain of a function rational functions 
Derivatives of Logarithmic Functions
Calculus The Derivative
How to infer the derivative of the natural log function using a calculator investigation.
derivative formula limits derivative the number e numerical approximation of the derivative natural logarithm 
Continuity
Calculus Limits and Continuity
How to determine whether a function f(x) is continuous at a particular point x=a.
limits definition of a function continuous at a point domain of a function 
Chain Rule: The General Logarithm Rule
Calculus Techniques of Differentiation
How to differentiate a composite function when the outside function is the natural logarithm.
chain rule logarithmic functions properties of logarithms derivative of natural log 
The Product Rule
Calculus Techniques of Differentiation
How to differentiate a product of two functions.
differentiation derivative formula power functions the product rule of derivatives 
Substitutions Involving e^x or ln(x)
Calculus Antiderivatives and Differential Equations
How to use the method of substitution when the antiderivatives involve e^x or ln[x].
substitution antidifferentiation exponential functions logarithmic functions power functions 
Antidifferentiation
Calculus Antiderivatives and Differential Equations
How to find an antiderivative of a function.
antiderivative derivative