For anyone who uses TI-85's: Have you noticed that entering something like
results in an imaginary number? It's one of the cube roots of 64, as is the expected "real" answer, 4. When I first noticed this a year or so ago, I thought it quirky but a great opportunity to talk to students about why it's a correct answer, even though it's not what we expect. And, the calculator's behavior can be circumvented by entering
(-8)^(2)^(1/3) or, vice versa (-8)^(1/3)^(2)
There's another development: the calculator won't produce a graph of, or evaluate, the derivative of a cube root function over the values for which the argument of the cube root is negative. If you've never noticed this, try graphing or evaluating the derivative of y = x^(1/3) using the "der1" function.
The "nder" , or "numerical derivative" works okay. But I'm curious as to why the TI-85 does this...I've noticed that, on the other hand, the TI-86 is well-behaved on this matter, so somebody at TI has noticed, I suppose. Perhaps I should be sending this post to TI...anybody got the address?