Pages similar to: Approximating a nonlinear function by a linear function
- Introduction to differentiability in higher dimensions
An introduction to the basic concept of the differentiability of a function of multiple variables. Discussion centers around the existence of a tangent plane to a function of two variables. - The multivariable linear approximation
Introduction to the linear approximation in multivariable calculus and why it might be useful. - Examples of calculating the derivative
Examples showing how to calculate the derivative and linear approximation of multivariable functions. - The definition of differentiability in higher dimensions
The definition of differentiability for multivariable functions. Informal derivation designed to give intuition behind the condition for a function to be differentiable. - Introduction to Taylor's theorem for multivariable functions
Development of Taylor's polynomial for functions of many variables. - The idea of the derivative of a function
The derivative of a function as the slope of the tangent line. - Derivatives of polynomials
How to compute the derivative of a polynomial. - Derivatives of more general power functions
How to compute the derivative of power functions. - A refresher on the quotient rule
How to compute the derivative of a quotient. - A refresher on the product rule
How to compute the derivative of a product. - A refresher on the chain rule
How to compute the derivative of a composition of functions. - Related rates
Calculating one derivative in terms of another derivative. - Intermediate Value Theorem, location of roots
Using the Intermediate Value Theorem to find small intervals where a function must have a root. - Newton's Method
A method to approximate the roots to an equation. - Derivatives of transcendental functions
A list of formulas for taking derivatives of exponential, logarithm, trigonometric, and inverse trigonometric functions. - L'Hospital's rule
A way to simplify evaluation of limits when the limit is an indeterminate form. - The second and higher derivatives
Taking derivatives multiple times to calculate the second or higer derivative. - Inflection points, concavity upward and downward
Finding points where the second derivative changes sign. - Developing intuition about the derivative
An intuitive exploration into the properties of the derivative, illustrated by interactive graphics. - Exploring the derivative of the exponential function
A guided tour into the reasons that the derivative of the exponential function with base e is the function itself.