# Calculators - Calculus I

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## MathGrapher: Graphing Calculator-Function Grapher

A free online 2D graphing calculator (plotter), or curve calculator, that can plot piecewise, linear, quadratic, cubic, quartic, polynomial, trigonometric, hyperbolic, exponential, logarithmic, inverse functions given in different forms: explicit, implicit, polar, and parametric. It can also graph conic sections, arbitrary inequalities or systems of inequalities, slope fields (vector fields or direction fields), and visualize the Riemann sum. The plots can be styled and customized according to needs.

To plot a 3d graph, use the 3d grapher.

## Online Derivative Calculator with Steps

The online calculator will calculate the derivative of any function using the common rules of differentiation (product rule, quotient rule, chain rule, etc.), with steps shown. It can handle polynomial, rational, irrational, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic functions. Also, it will evaluate the derivative at the given point if needed. It also supports computing the first, second, and third derivatives, up to 10.

## Instantaneous Rate of Change Calculator

This calculator will find the instantaneous rate of change of the given function at the given point, with steps shown.

## Average Rate of Change Calculator

The calculator will find the average rate of change of the given function on the given interval, with steps shown.

## Difference Quotient Calculator

The calculator will find the difference quotient for the given function, with steps shown.

## Limit Calculator

This free calculator will try to find the limit (two-sided or one-sided, including left and right) of the given function at the given point (including infinity), with steps shown.

## Differential of a Function Calculator

For the given function $$$y=f(x)$$$, point $$$x_0$$$ and argument change $$$\Delta x_0$$$, the calculator will find the differential $$$dy$$$ and the function change $$$\Delta y$$$, with steps shown.

## Linear Approximation Calculator

The calculator will find the linear approximation to the explicit, polar, parametric, and implicit curve at the given point, with steps shown.

## Quadratic Approximation Calculator

The calculator will find the quadratic approximation to the given function at the given point, with steps shown.

## Tangent Line Calculator

The calculator will find the tangent line to the explicit, polar, parametric and implicit curve at the given point, with steps shown.

It can handle horizontal and vertical tangent lines as well.

The tangent line is perpendicular to the normal line.

## Normal Line Calculator

The calculator will find the normal line to the explicit, polar, parametric and implicit curve at the given point, with steps shown.

It can handle horizontal and vertical normal lines as well.

The normal line is perpendicular to the tangent line.

## Taylor and Maclaurin (Power) Series Calculator

The calculator will find the Taylor (or power) series expansion of the given function around the given point, with steps shown. You can specify the order of the Taylor polynomial. If you want the Maclaurin polynomial, just set the point to $$$0$$$.

## Implicit Differentiation Calculator with Steps

The implicit differentiation calculator will find the first and second derivatives of an implicit function treating either $$$y$$$ as a function of $$$x$$$ or $$$x$$$ as a function of $$$y$$$, with steps shown.

## Asymptote Calculator

The calculator will try to find the vertical, horizontal, and slant asymptotes of the function, with steps shown.

## Function Calculator

The calculator will try to find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical (stationary) points, extrema (minimum and maximum, local, relative, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the single-variable function. The interval can be specified. Parity will also be determined.

## Domain and Range Calculator

The calculator will find the domain and range of the single-variable function.

## Critical Points and Extrema Calculator

The calculator will try to find the critical (stationary) points, the relative (local) and absolute (global) maxima and minima of the single variable function. The interval can be specified.

## Inflection Points and Concavity Calculator

The calculator will try to find the intervals of concavity and the inflection points of the given function.

## Mean Value Theorem Calculator

The calculator will find all numbers $$$c$$$ (with steps shown) that satisfy the conclusions of the mean value theorem for the given function on the given interval. Rolle's theorem is a special case of the mean value theorem (when $$$f(a)=f(b)$$$).

## Secant Line Calculator

The calculator will find the equation of the secant line that intersects the given curve at the given points, with steps shown.