Section 2
Applications of Differentiation
By Boundless
A linear approximation is an approximation of a general function using a linear function.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17941/raw/extrema-example-original.jpg)
Maxima and minima are critical points on graphs and can be found by the first derivative and the second derivative.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17940/raw/mvt2.jpg)
The MVT states that for a function continuous on an interval, the mean value of the function on the interval is a value of the function.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17933/square/of-sliding-derivative-line.gif)
The shape of a graph may be found by taking derivatives to tell you the slope and concavity.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17932/square/asymptote03.jpg)
The asymptotes are computed using limits and are classified into horizontal, vertical and oblique depending on the orientation.
Curve sketching is used to produce a rough idea of overall shape of a curve given its equation without computing a detailed plot.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17947/square/220px-ti-84-plus-graphing.jpeg)
Graphics can be created by hand, using computer programs, and with graphing calculators.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17946/square/220px-maximumparaboloid.jpg)
Mathematical optimization is the selection of a best element (with regard to some criteria) from some set of available alternatives.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17945/square/300px-newtoniteration-ani.gif)
Newton's Method is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17944/raw/extrema-example-original.jpg)
The second derivative test is a criterion for determining whether a given critical point is a local maximum or a local minimum.
![Thumbnail](../../../../../../figures.boundless-cdn.com/17943/square/diferencial-de-una-funcion.jpg)
Differentials are the principal part of the change in a function