Functions and their Curvatures
motivated by discussions on a Calculus Forum
Here's a neat type of problem:
  • You present the graph of some function, for example
  • Then you provide a gaggle of other functions and ask:
    Which is the graph of the second derivative of f(x)?
  • Then you ...
>Huh? What do the choices look like?
Like this:

>And the answer is ... ?
That's your problem, not mine.

Anyway, I got me a spreadsheet that'll help design such problems ... like so:

Just click on the picture to download the Excel spreadsheet.

You type in some neat f(x) and click a button and the spreadsheet generates four graphs -- the first four derivates of the function.
So that the "correct" answer won't always be in the same spot, you can press F9 to mix 'em up.
Further, in case you can't think of any sexy functions, there's a flock of 'em available. Just click on one of the buttons.

Note: There are some problems you can try. Just click here!

>Sounds like fun, but what if I wanted to print some of these problems?
Good point!
Okay, here's another spreadsheet:

It's got a few functions, f , g, h and k, and you can choose to print four such questions.
The questions, such as Which is the graph if f ''(x)?, can be changed to (for example) Which is the graph if f '(x)? ... or whatever.
Note, too, that there are a bunch of choices for each function (in case you're too lazy to type them into cells F1 to F4).
The printout will look like this:

See: Math Stuff