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  2. Derivative test - Wikipedia

    en.wikipedia.org/wiki/Derivative_test

    The higher-order derivative test or general derivative test is able to determine whether a function's critical points are maxima, minima, or points of inflection for a wider variety of functions than the second-order derivative test. As shown below, the second-derivative test is mathematically identical to the special case of n = 1 in the ...

  3. Second partial derivative test - Wikipedia

    en.wikipedia.org/wiki/Second_partial_derivative_test

    Thus, the second partial derivative test indicates that f(x, y) has saddle points at (0, −1) and (1, −1) and has a local maximum at (,) since = <. At the remaining critical point (0, 0) the second derivative test is insufficient, and one must use higher order tests or other tools to determine the behavior of the function at this point.

  4. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    The second derivative test can still be used to analyse critical points by considering the eigenvalues of the Hessian matrix of second partial derivatives of the function at the critical point. If all of the eigenvalues are positive, then the point is a local minimum; if all are negative, it is a local maximum.

  5. Second derivative - Wikipedia

    en.wikipedia.org/wiki/Second_derivative

    The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.

  6. Symmetry of second derivatives - Wikipedia

    en.wikipedia.org/wiki/Symmetry_of_second_derivatives

    In the middle of the 18th century, the theory of differential forms was first studied in the simplest case of 1-forms in the plane, i.e. +, where and are functions in the plane. The study of 1-forms and the differentials of functions began with Clairaut's papers in 1739 and 1740.

  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 f is positive. ...

  8. One Knock. Two Men. One Bullet. - The Huffington Post

    projects.huffingtonpost.com/bryan-yeshion...

    Bryan Yeshion Schneps, a 21‑year‑old Temple University student, tried to prevent his attackers from gaining entry. He pressed his hands, his shoulders, his knees, his feet, the full weight of his 6'1", 180‑pound body against the door. But his stamina wore thin, and the door swung free. Bryan cried for help.

  9. Fermat's theorem (stationary points) - Wikipedia

    en.wikipedia.org/wiki/Fermat's_theorem...

    The complication is that in 1 dimension, one can either move left or right from a point, while in higher dimensions, one can move in many directions. Thus, if the derivative does not vanish, one must argue that there is some direction in which the function increases – and thus in the opposite direction the function decreases. This is the only ...

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