The TI-30X Pro MathPrint™ calculates the (approximate) numeric derivative of an expression at a point given a tolerance for the numeric method. (See the About the Numeric Derivative at a Point section for more information.)
MathPrint™ Mode
% A pastes the numeric derivative template from the keypad to calculate the numeric derivative with the default tolerance H is 1EM5.
Example
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% A |
% A z F T 5 z " " M 1 < |
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To change the default tolerance, H, and observe how the tolerance plays a role in the numeric solution, paste the numeric derivative from the menu location, d MATH 7:nDeriv(, where the numeric derivative template will paste with the option to modify the tolerance as needed for an investigation of the numeric derivative result.
Example
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d MATH 7:nDeriv( with optional tolerance |
d 7 z F T 5 z " " M 1 " 1 E M 5 < |
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Classic Mode or Entry
In Classic mode or in classic edit lines, the nDeriv( command will paste from the keypad or MATH menu.
Syntax: nDeriv(expression,variable,point[,tolerance]) where tolerance is optional and the default H is 1EM5.
Example
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% A or d MATH 7:nDeriv( |
% A z F T 5 z % ` z % ` M 1 ) < |
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About the Numeric Derivative at a Point
The numeric derivative at a point command, nDeriv( or d/dx, uses the symmetric difference quotient method. This method approximates the numerical derivative at a given point as the slope of the secant line about the point.
As H becomes smaller, the approximation usually becomes more accurate to approximate the slope of the tangent line at the given point x.
| • | Because of the method used to calculate the numeric derivative at a point, the calculator can return a false derivative value at a non-differentiable point. |
| • | Always have some knowledge of the function behavior near the point by using a table of values near the point (or a graph of the function). |
Problem
Find the slope of the tangent line to the function f(x) = x2 - 4x at x = 2. What do you notice?
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% A z F U 4 z " " 2 < |
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