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To calculate the derivative of a function, one must use techniques from the differential branch of calculus. This branch of calculus is related to the integral branch by the first fundamental theorem of calculus: ''differentiation'' (the process of finding a derivative) ''is the reverse process of [[integral|integration]]'' (the process of finding an integral).

To calculate the derivative of a function, one must use techniques from the differential branch of calculus. This branch of calculus is related to the integral branch by the first fundamental theorem of calculus: ''differentiation'' (the process of finding a derivative) ''is the reverse process of [[integral|integration]]'' (the process of finding an integral).

In mathematics, 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.

In mathematics, 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.

[[Category:Calculus]]

[[Category:Calculus]]

[[Category:Mathematics]]

[[Category:Mathematics]]