Calculus
Textbooks
Boundless Calculus
Derivatives and Integrals
Calculus Textbooks Boundless Calculus Derivatives and Integrals
Calculus Textbooks Boundless Calculus
Calculus Textbooks
Calculus

Section 2

Applications of Differentiation

Book Version 1
By Boundless
Boundless Calculus
Calculus
by Boundless
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11 concepts
Linear Approximation

A linear approximation is an approximation of a general function using a linear function.

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Maximum and Minimum Values

Maxima and minima are critical points on graphs and can be found by the first derivative and the second derivative.

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The Mean Value Theorem, Rolle's Theorem, and Monotonicity

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.

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Derivatives and the Shape of the Graph

The shape of a graph may be found by taking derivatives to tell you the slope and concavity.

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Horizontal Asymptotes and Limits at Infinity

The asymptotes are computed using limits and are classified into horizontal, vertical and oblique depending on the orientation.

Curve Sketching

Curve sketching is used to produce a rough idea of overall shape of a curve given its equation without computing a detailed plot.

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Graphing on Computers and Calculators

Graphics can be created by hand, using computer programs, and with graphing calculators.

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Optimization

Mathematical optimization is the selection of a best element (with regard to some criteria) from some set of available alternatives.

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Newton's Method

Newton's Method is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

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Concavity and the Second Derivative Test

The second derivative test is a criterion for determining whether a given critical point is a local maximum or a local minimum.

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Differentials

Differentials are the principal part of the change in a function $y = f(x)$ with respect to changes in the independent variable.

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