Math Insight

Pages similar to: Newton's Method

• Intermediate Value Theorem, location of roots
  Using the Intermediate Value Theorem to find small intervals where a function must have a root.
• Multivariable chain rule examples
  Examples demonstrating the chain rule for multivariable functions.
• The multidimensional differentiability theorem
  Discussion of theorem that gives conditions which guarantee that a multivariable function is differentiable.
• Non-differentiable functions must have discontinuous partial derivatives
  A visual tour demonstrating discontinuous partial derivatives of a non-differentiable function, as required by the differentiability theorem.
• A differentiable function with discontinuous partial derivatives
  Illustration that discontinuous partial derivatives need not exclude a function from being differentiable.
• Special cases of the multivariable chain rule
  Illustrations of different special cases of the multivariable chain rule and their relationship to the general case.
• The gradient vector
  The gradient vector is the matrix of partial derivatives of a scalar valued function viewed as a vector.
• 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.
• 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.
• Approximating a nonlinear function by a linear function
  The secant line and tangent line are two ways to approximate a nonlinear function by a linear one.
• Developing intuition about the derivative
  An intuitive exploration into the properties of the derivative, illustrated by interactive graphics.

Back to: Newton's Method