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  2. Five-point stencil - Wikipedia

    en.wikipedia.org/wiki/Five-point_stencil

    An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".

  3. Derivative test - Wikipedia

    en.wikipedia.org/wiki/Derivative_test

    The first-derivative test depends on the "increasing–decreasing test", which is itself ultimately a consequence of the mean value theorem. It is a direct consequence of the way the derivative is defined and its connection to decrease and increase of a function locally, combined with the previous section.

  4. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.

  5. Maximum and minimum - Wikipedia

    en.wikipedia.org/wiki/Maximum_and_minimum

    (2nd derivative is 0 at that point.) Unique global maximum at x = e. (See figure at right) x −x: Unique global maximum over the positive real numbers at x = 1/e. x 3 /3 − x: First derivative x 2 − 1 and second derivative 2x. Setting the first derivative to 0 and solving for x gives stationary points at −1 and +1. From the sign of the ...

  6. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    The graph of =, with a straight line that is tangent to (,). The slope of the tangent line is equal to . (The axes of the graph do not use a 1:1 scale.) The derivative of a function is then simply the slope of this tangent line.

  7. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    The logarithmic derivative is another way of stating the rule for differentiating the logarithm of a function (using the chain rule): (⁡) ′ = ′, wherever is positive. Logarithmic differentiation is a technique which uses logarithms and its differentiation rules to simplify certain expressions before actually applying the derivative.

  8. Numerical differentiation - Wikipedia

    en.wikipedia.org/wiki/Numerical_differentiation

    The classical finite-difference approximations for numerical differentiation are ill-conditioned. However, if is a holomorphic function, real-valued on the real line, which can be evaluated at points in the complex plane near , then there are stable methods.

  9. Differentiable function - Wikipedia

    en.wikipedia.org/wiki/Differentiable_function

    A similar formulation of the higher-dimensional derivative is provided by the fundamental increment lemma found in single-variable calculus. If all the partial derivatives of a function exist in a neighborhood of a point x 0 and are continuous at the point x 0, then the function is differentiable at that point x 0.