
Two young mathematicians discuss a ‘Jeopardy!’ version of calculus.

Check out this dialogue between two calculus students (based on a true story):
Devyn
(Pretending to be Alex Trebek) I’ve got a new costume.
Riley
Whoa! You look just like Trebek!
Devyn
In Jeopardy!, I, Trebek, give you an answer, and you must tell me the question.
Riley
Uh Alex, ‘What are the rules of Jeopardy!?’
Devyn
Ha. Exactly! Let’s play a different version where I’ll tell you a derivative, and you tell me the function. Are you ready?
Riley
I’ll take “Formulas for slope” for $\200$.
Devyn
$3\cdot e^{3x}$
Riley
I’ve got an answer! Actually, I’ve got three different answers, I mean questions!
(a)
“What’s the derivative of $e^{3x}$?
(b)
“What’s the derivative of $e^{3x}+1$?
(c)
“What’s the derivative of $e^{3x}-1$?
Devyn
Hmmm. Now I’m not sure which one it was.
Riley
What about if you had given me $\frac {\sin (x)}{x}$?
How many functions whose derivative is $3\cdot e^{3x}$ are there?
Zero One Two Three Four Infinitely many
How many functions whose derivative is $3\cdot e^{3x}$ that equal $1$ at $x=0$ are there?
Zero One Two Three Four Infinitely many