### Taylor Polynomials

Graphs a function f(x) and the Taylor polynomial approximations to f(x) up to degree 4 for a given c value (the center point for the Taylor polynomials).
How to use   ||   Examples   ||   Other Notes

Try the Derivative Calculator.
How to use
• Enter a function f (x) in the text input field marked "f (x)=" (Example: f (x)=ex)
• Click the "Graph" button (this button also refreshes the graph)
• Enter the derivativs f '(x), f '(x), etc., in the text input fields marked "f '(x)=", "f ''(x)=", etc. (up to the fourth derivative) (Example: f '(x)=f ''(x)=...=ex)
• Select a c value, the center point for the Taylor polynomials (Example: c=1)
This can be done in either of two ways:
• Click and drag the mouse on the graph -- value of c corresponds to horizontal mouse position on graph
• Enter the value in the text input field marked "c=" and click the "Graph" button to refresh
• To erase the graph and all input fields, click the "Clear" button
The text input fields marked "f (x)=", "f '(x)=", etc., can accept a wide variety of expressions to represent functions. The text input field marked "c=" can accept a real number in decimal notation. The buttons under the graph allow various manipulations of the graph coordinates.

For assistance computing the derivatives f '(x), f ''(x), etc., try the Derivative Calculator.

Examples
 Exponential: f (x) = ex f '(x) = ex f ''(x) = ex f '''(x) = ex f ''''(x) = ex      c = 1 Trigonometric: f (x) = sin x f '(x) = cos x f ''(x) = -sin x f '''(x) = -cos x f ''''(x) = sin x c = 0

Other Notes
The degree one Taylor polynomial (tangent line) will be shown in blue, degree two in red, degree three in green, and degree four in orange.