In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local...

In mathematics, the second partial derivative test is a method in multivariable calculus used to determine if a critical point of a function is a local...

stationary points, where the first derivative or the gradient of the objective function is zero (see first derivative test). More generally, they may be...

Implicit differentiation Stationary point Maxima and minima First derivative test Second derivative test Extreme value theorem Differential equation Differential...

left). The phase line is identical in form to the line used in the first derivative test, other than being drawn vertically instead of horizontally, and...

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...

local minimum, or neither by using the first derivative test, second derivative test, or higher-order derivative test, given sufficient differentiability...

four kinds, by the first derivative test: a local minimum (minimal turning point or relative minimum) is one where the derivative of the function changes...

respectively, there.) This is called the second derivative test. An alternative approach, called the first derivative test, involves considering the sign of the...

In calculus, an optimal solution is sought using the first derivative test: the first derivative of the function being optimized is equated to zero, and...

the first derivative test, according to which the monotonicity of a function can be defined as the inequality of function's first derivative greater or...

second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f. Informally, the second derivative can be...

protein derivative (PPD) tine test. Common brand names of the test include Aplisol, Aplitest, Tuberculin PPD TINE TEST, and Tubersol. This test uses a...

conditions, also known as the Kuhn–Tucker conditions, are first derivative tests (sometimes called first-order necessary conditions) for a solution in nonlinear...

g''(x),\dots ,g^{(n-k+1)}(x)\right).} first-degree polynomial first derivative test The first derivative test examines a function's monotonic properties...

protein derivative) is a tool for screening for tuberculosis (TB) and for tuberculosis diagnosis. It is one of the major tuberculin skin tests used around...

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held...

the logarithmic derivative of a function f is defined by the formula f ′ f {\displaystyle {\frac {f'}{f}}} where f′ is the derivative of f. Intuitively...

standard notation for differentiation. Instead, several notations for the derivative of a function or a dependent variable have been proposed by various mathematicians...

the Fréchet derivative is a derivative defined on normed spaces. Named after Maurice Fréchet, it is commonly used to generalize the derivative of a real-valued...

variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional (a functional in this...

classically differentiable, a weak derivative may be defined by means of integration by parts. First define test functions, which are infinitely differentiable...

+T)/\tau } in the first segment and by ( τ − T ) / τ {\displaystyle (\tau -T)/\tau } in the second segment, which changes all time derivatives by the dilation...

exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The exterior derivative was first described...

In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let h ( x ) = f (...

rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a...

protein derivative, is a combination of proteins that are used in the diagnosis of tuberculosis. This use is referred to as the tuberculin skin test and is...

vector-valued function of several variables is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables...

highly classified United States Air Force (USAF) facility within the Nevada Test and Training Range in southern Nevada, 83 miles (134 km) north-northwest...

more can be said from the point of view of Morse theory. The second-derivative test for functions of one and two variables is simpler than the general...