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...

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...

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

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

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

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...

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

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...

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...

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...

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...

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

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...

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...

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...

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

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...

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...

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...

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

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 (...

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

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...

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

asserts that, if a real function f has a continuous derivative near a point where its derivative is nonzero, then, near this point, f has an inverse function...

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...

formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. More precisely...

The following are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)}...