Derivative testIn 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 proved mathematically by Fermat's theorem of stationary points. The first-derivative test examines a function's monotonic properties (where the function is increasing or decreasing), focusing on a particular point in its domain.
Total derivativeIn mathematics, the total derivative of a function f at a point is the best linear approximation near this point of the function with respect to its arguments. Unlike partial derivatives, the total derivative approximates the function with respect to all of its arguments, not just a single one. In many situations, this is the same as considering all partial derivatives simultaneously. The term "total derivative" is primarily used when f is a function of several variables, because when f is a function of a single variable, the total derivative is the same as the ordinary derivative of the function.
EnstatiteEnstatite is a mineral; the magnesium endmember of the pyroxene silicate mineral series enstatite (MgSiO3) – ferrosilite (FeSiO3). The magnesium rich members of the solid solution series are common rock-forming minerals found in igneous and metamorphic rocks. The intermediate composition, (Mg,Fe)SiO3, has historically been known as hypersthene, although this name has been formally abandoned and replaced by orthopyroxene. When determined petrographically or chemically the composition is given as relative proportions of enstatite (En) and ferrosilite (Fs) (e.
BorateA borate is any of a range of boron oxyanions, anions containing boron and oxygen, such as orthoborate , metaborate , or tetraborate ; or any salt of such anions, such as sodium metaborate, and borax . The name also refers to esters of such anions, such as trimethyl borate . Borate ions occur, alone or with other anions, in many borate and borosilicate minerals such as borax, boracite, ulexite (boronatrocalcite) and colemanite. Borates also occur in seawater, where they make an important contribution to the absorption of low frequency sound in seawater.
