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  2. Inflection point - Wikipedia

    en.wikipedia.org/wiki/Inflection_point

    An example of a stationary point of inflection is the point (0, 0) on the graph of y = x 3. The tangent is the x-axis, which cuts the graph at this point. An example of a non-stationary point of inflection is the point (0, 0) on the graph of y = x 3 + ax, for any nonzero a. The tangent at the origin is the line y = ax, which cuts the graph at ...

  3. Titration curve - Wikipedia

    en.wikipedia.org/wiki/Titration_curve

    The equivalence point on the graph is where all of the starting solution (usually an acid) has been neutralized by the titrant (usually a base). It can be calculated precisely by finding the second derivative of the titration curve and computing the points of inflection (where the graph changes concavity ); however, in most cases, simple visual ...

  4. Second derivative - Wikipedia

    en.wikipedia.org/wiki/Second_derivative

    If the second derivative of a function changes sign, the graph of the function will switch from concave down to concave up, or vice versa. A point where this occurs is called an inflection point. Assuming the second derivative is continuous, it must take a value of zero at any inflection point, although not every point where the second ...

  5. Curve fitting - Wikipedia

    en.wikipedia.org/wiki/Curve_fitting

    Low-order polynomials tend to be smooth and high order polynomial curves tend to be "lumpy". To define this more precisely, the maximum number of inflection points possible in a polynomial curve is n-2, where n is the order of the polynomial equation. An inflection point is a location on the curve where it switches from a positive radius to ...

  6. Curve sketching - Wikipedia

    en.wikipedia.org/wiki/Curve_sketching

    An x value where the y value of the red, or the blue, curve vanishes (becomes 0) gives rise to a local extremum (marked "HP", "TP"), or an inflection point ("WP"), of the black curve, respectively. In geometry , curve sketching (or curve tracing ) are techniques for producing a rough idea of overall shape of a plane curve given its equation ...

  7. Sigmoid function - Wikipedia

    en.wikipedia.org/wiki/Sigmoid_function

    A sigmoid function is a bounded, differentiable, real function that is defined for all real input values and has a non-negative derivative at each point [1] [2] and exactly one inflection point. Properties

  8. Critical point (mathematics) - Wikipedia

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

    The x-coordinates of the red circles are stationary points; the blue squares are inflection points. In mathematics, a critical point is the argument of a function where the function derivative is zero (or undefined, as specified below). The value of the function at a critical point is a critical value. [1]

  9. Derivative test - Wikipedia

    en.wikipedia.org/wiki/Derivative_test

    In conjunction with the extreme value theorem, it can be used to find the absolute maximum and minimum of a real-valued function defined on a closed and bounded interval. In conjunction with other information such as concavity, inflection points, and asymptotes, it can be used to sketch the graph of a function.