culture shock or the doubtful decidiness of mathem

[allfred]

Hello

Introduction
I am retired, but from time to time I am asked about Calculus problems, so recently because of differetiability of functions, more exactly about one with an upright tangent.
Problem solved and lied ad acta (as I thought).

Interlude
Because of curiosity, I paged through L. Leithold\'s Calculus (solution) book. There was an interesting problem
f(x)=(x^3-3x^2+4)^(1/3)
which remembered me, what happened a while ago. A useful problem I thought and instantly I entered it into my (german, I am from there) function plotter but

Shock I
the used domain was from -1 ... inf (Leithold\'s (and mine too) however run from -inf ... + inf), below (-1) the function wasn\'t  plotted, because the function isn\'t defined for x<(-1). informed  the program cool!

Shocks xxx ... yyy
a second program and one from USA showed the same picture, in contradiction to Leithold. (Similar reasons).

Esperance
I contacted the authors: one told me, he\'s aware of this problerm, but the programming language doesn\'t accept neg roots and the other one sent me a definition of Bronstein\'s  Handbook of Mathematics, the argument under the root sign must be >0 can be red there. Obviously all ok!

Perplexity
Then I rememberd Autograph, and this program showed the same result as Leithold. So the score is 2:3. But it\'s not soccer. I believed maths to be a distinct science.

Are there regionally different aspects of one and the same problem?

What do you think about this?

thanks
Allfred
     

[Simon]

Dear Alfred,

The reason some plotters do not plot the graph correctly is that they compute x^(1/3) as exp((1/3)ln(x)) and ln(x) is not defined for x < 0.

The square root function has domain [0, inf) (provided we\'re sticking to the real numbers) but the cube root function has domain (-inf, inf).  The argument certainly does not need to be positive.

You may be interested to know that we are about to release a German version of Autograph.  

Hope this helps,

Simon

[Simon]

Dear Alfred,

As an addition to my earlier comments, I thought I would describe a neat way to look at functions with upright tangents in Autograph.

1. Click Function Definitions... and set f(x) = (x