# Not sure what this question means

• March 26th 2010, 03:09 PM
dwsmith
Not sure what this question means
Make a conjecture about the nth derivative of the function f(x)=e^(ax). This conjecture should be written as a self contained proposition including an appropriate quantifier.

That does this last sentence mean?
• March 26th 2010, 03:34 PM
skeeter
Quote:

Originally Posted by dwsmith
Make a conjecture about the nth derivative of the function f(x)=e^(ax). This conjecture should be written as a self contained proposition including an appropriate quantifier.

That does this last sentence mean?

$f(x) = e^{ax}$

$f'(x) = ae^{ax}
$

$f''(x) = a^2e^{ax}$

$f'''(x) = a^3e^{ax}$

do you see a pattern to construct an expression for $f^{n}(x)$ so that you may answer within the given guidelines ?
• March 26th 2010, 03:38 PM
dwsmith
I understand what is happening with the function. It is the last sentence I am not sure what they are asking for.

This conjecture should be written as a self contained proposition including an appropriate quantifier.
• March 26th 2010, 03:56 PM
skeeter
Quote:

Originally Posted by dwsmith
I understand what is happening with the function. It is the last sentence I am not sure what they are asking for.

This conjecture should be written as a self contained proposition including an appropriate quantifier.

then write what you understand and ask the questions ...

is it self-contained?

does it possess an appropriate quantifier?

... don't get too caught up in the high-dollar verbage.
• March 27th 2010, 03:45 AM
HallsofIvy
"Appropriate quantifier": is your statement true for all a and x or do there exist some values of a and/or x for which it is true?