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The TI-30X Pro MathPrint™ calculates the (approximate) numerical derivative of an expression at a point given a tolerance for the numerical method. (See the About the Numerical Derivative at a Point section for more information.)
% A pastes the numerical derivative template from the keypad to calculate the numerical derivative with the default tolerance H is 1EM5.
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To change the default tolerance, H, and observe how the tolerance plays a role in the numerical solution, paste the numerical derivative from the menu location, d MATH 7:nDeriv(, where the numerical derivative template will paste with the option to modify the tolerance as needed for an investigation of the numerical derivative result.
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d MATH 7:nDeriv( with optional tolerance |
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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.
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% A or d MATH 7:nDeriv( |
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The numerical 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 numerical derivative at a point, the calculator can return a false derivative value at a non-differentiable point. |
| • | Always have some knowledge of the function behaviour near the point by using a table of values near the point (or a graph of the function). |
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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