# Thread: Not sure what this question means

1. ## 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?

2. 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 ?

3. 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.

4. 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.

5. "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?