Two young mathematicians think about limits.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley, I want to play a game!
Riley
Ok. What’s the game?
Devyn
I’m thinking of a function. You are trying to figure out the output value of my function when the input is .
Riley
So if I call your function , I win if I can guess , right? What information do I have to work with?
Devyn
Right! You can ask for the output values for three different input values that are not . Any other input is ok.
Riley
I’m in! What’s ?
Devyn
When the input is , the output is , so . That’s one value down, two more. What do you want to know next?
Riley
What’s ?
Devyn
I think I see your strategy. .
Riley
With my last value, I’ll ask for .
Devyn
. Was that enough information for you to guess ?
What is ?
Not enough information to tell.
Which of the following best describes Riley’s strategy to find the value?
Differentiation. Chain Rule. Limit. Optimization. None of these.
Which of the following properties would have given Riley a better chance at guessing the value?
Differentiability. Continuity. The function has an absolute maximum value. None of these.