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  2. Linear approximation - Wikipedia

    en.wikipedia.org/wiki/Linear_approximation

    Tangent line at (a, f(a)) In mathematics , a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function ). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations.

  3. Tangent - Wikipedia

    en.wikipedia.org/wiki/Tangent

    This leads to the definition of the slope of the tangent line to the graph as the limit of the difference quotients for the function f. This limit is the derivative of the function f at x = a, denoted f ′(a). Using derivatives, the equation of the tangent line can be stated as follows: = + ′ ().

  4. Critical point (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Critical_point_(mathematics)

    The graph of f is a concave up parabola, the critical point is the abscissa of the vertex, where the tangent line is horizontal, and the critical value is the ordinate of the vertex and may be represented by the intersection of this tangent line and the y-axis. The function () = / is defined for all x and differentiable for x ≠ 0, with the ...

  5. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    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. The tangent line is the best linear approximation of the function near that input value.

  6. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

  7. Partial derivative - Wikipedia

    en.wikipedia.org/wiki/Partial_derivative

    To find the slope of the line tangent to the function at P(1, 1) and parallel to the xz-plane, we treat y as a constant. The graph and this plane are shown on the right. Below, we see how the function looks on the plane y = 1. By finding the derivative of the equation while assuming that y is a constant, we find that the slope of f at the point ...

  8. Contact (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Contact_(mathematics)

    An osculating curve from a given family of curves is a curve that has the highest possible order of contact with a given curve at a given point; for instance a tangent line is an osculating curve from the family of lines, and has first-order contact with the given curve; an osculating circle is an osculating curve from the family of circles ...

  9. Folium of Descartes - Wikipedia

    en.wikipedia.org/wiki/Folium_of_Descartes

    The curve was first proposed and studied by René Descartes in 1638. [1] Its claim to fame lies in an incident in the development of calculus.Descartes challenged Pierre de Fermat to find the tangent line to the curve at an arbitrary point since Fermat had recently discovered a method for finding tangent lines.