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Accept all. Secant Lines In this activity, students will observe the slopes of the secant and tangent line as a point on the function approaches the point of tangency. Standards Textbook. Download Extrema and Concavity Students learn how to find and label extrema using first and second derivatives, be able to inspect a graph and determine which extrema the function has, and be able to use trace, fMin, and fMax to verify the computed answers and find critical values for parametric functions.
Zooming In On Local Linearity In this activity, students will explore the behavior of various functions by zooming in on their graphs. Using Slope Fields Students identify whether a slope field approximately reflects a differential equation. Download 5, Students create a slope field for a given differential equation Standards Textbook.
Investigating the Derivatives of Some Common Functions In this activity, students will investigate the derivatives of sine, cosine, natural log, and natural exponential functions by examining the symmetric difference quotient at many points.
Download 4, Graphing Relationships In this activity, students explore information about a graph based on the first and second derivatives. This image shows the derivative at various points as the slope of a tangent line. When the derivative is positive, the line is green. When the derivative is negative, the line is red. When it is zero, the line is black.
Unfortunately, this function only returns the derivative of a single point. While there is no built-in function on the TI Plus and TI Plus to take a derivative in general, you can read more about using an application to enable this functionality here. Next, enter the function you want to differentiate, press , , enter the function variable, and add a closing parenthesis to finish the expression. Instead of calculating a specific value, the calculator displays a general expression for the derivative.
You can also specify a specific x value to calculate the exact value of the derivative at a single point. You can also select the output of the derivative function to evaluate it at a single point. Your email address will not be published. For higher order derivatives, things only get worse. I remember that for some simple functions I could get 4 or 5 derivatives before it was just impossible to get anything meaningful because the calculator just doesn't have enough precision.
Incidentally, if you find the above method isn't precise enough, there's a ton of literature on numerical differentiation with better methods than the one laid out above. A good place to start would be the Wikipedia article on finite difference methods , of which the above formula is a not particularly good example.
No matter what, you're going to run into machine precision issues, but using a more sophisticated method will at least raise the accuracy until machine precision effects start to be important. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Collectives on Stack Overflow. Learn more.
Can TI Basic handle nth-order derivatives? Ask Question. Asked 8 years, 3 months ago. Active 8 years, 3 months ago. Viewed 3k times. Improve this question. Ky Leggiero Ky Leggiero Add a comment. Active Oldest Votes.
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