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Derivative test. 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 maximum, a local minimum, or a saddle point. Derivative tests can also give information about the concavity of a function. The usefulness of derivatives to find extrema is ...
In calculus, a function defined on a subset of the real numbers with real values is called monotonic if it is either entirely non-decreasing, or entirely non-increasing. [2] That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is termed monotonically ...
In mathematics, Fermat's theorem (also known as interior extremum theorem) is a method to find local maxima and minima of differentiable functions on open sets by showing that every local extremum of the function is a stationary point (the function's derivative is zero at that point). Fermat's theorem is a theorem in real analysis, named after ...
In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero. [1][2][3] Informally, it is a point where the function "stops" increasing or decreasing (hence the name). For a differentiable function of several real ...
Marginal cost (MC) is the change in total cost per unit change in output or ∆ C /∆ Q. In the short run, production can be varied only by changing the variable input. Thus only variable costs change as output increases: ∆ C = ∆ VC = ∆ (wL). Marginal cost is ∆ (Lw)/∆ Q. Now, ∆ L /∆ Q is the reciprocal of the marginal product of ...
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation , where N is the quantity and λ ( lambda ) is a positive rate called the exponential decay constant , disintegration constant , [ 1 ] rate constant , [ 2 ] or ...
In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct points must have at least one point, somewhere between them, at which the slope of the tangent line is zero. Such a point is known as a stationary point.
Exponential growth is the inverse of logarithmic growth. Not all cases of growth at an always increasing rate are instances of exponential growth. For example the function grows at an ever increasing rate, but is very remote from growing exponentially. For example, when it grows at 3 times its size, but when it grows at 30% of its size.