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Line 20: − − Thus the derivative is a measurement of how a function changes when the values of its inputs vary. Derivatives are helpful in determining the [[maximum|maxima]] and [[minimum|minima]] of a function. For example, taking the derivative of a quadratic function will yield a linear function. The points at which this function equals zero are called ''critical'' points. Maxima and minima can occur at critical points, and can be verified to be a maximum or minimum by the ''second derivative test''. The second derivative is used to determine the [[concavity]], or curved shape of the graph. Where the concavity is positive, the graph curves upwards, and could contain a relative minimum. Where the concavity is negative, the graph curves downwards, and could contain a relative maximum. Where the concavity equals zero is said to be a point of ''inflection,'' meaning that it is a point where the concavity could be changing. Also, differentials have numerous applications in physics.
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In mathematics a '''derivative''' is measure of how functions change. Algebraic '''differentiation''' is an important part of [[calculus]], an essential branch of [[mathematics]] in the modern age. Differentiation can be used, for example, in [[mechanics]] to find the acceleration of an object from a velocity-time graph.
In mathematics a '''derivative''' is measure of how functions change. Algebraic '''differentiation''' is an important part of [[calculus]], an essential branch of [[mathematics]]. Differentiation can be used, for example, in [[mechanics]] to find the acceleration of an object from a velocity-time graph.
Essentially, differentiation is employed as a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph. These are a few examples of the applications of differentiation.
Essentially, differentiation is employed as a means to calculate the [[gradient]] or rate of change at a particular value for a given function, ''f''. Consequently, it can be used to calculate velocity from a displacement-time graph, or acceleration from a velocity-time graph. Furthermore, it can be used to calculate the rate of cooling from a temperature-time graph. These are a few examples of the applications of differentiation.
:<math>\frac{dy}{dx} = 6 x+2</math>
:<math>\frac{dy}{dx} = 6 x+2</math>
==Properties of the derivative==
==Properties of the derivative==