
Two young mathematicians look at graph of a function, its first derivative, and its second derivative.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley, check out this plot:
Riley
Whoa, that looks cool!
Devyn
I know! Anyway, someone told me that this was a graph of a function, its derivative, and the derivative of the derivative. Which one is which?
Riley
Hmmmmm. I’m not sure.
Which of the following is true?
Curve $$ is increasing when curve $$ is positive. Curve $$ is increasing when curve $$ is positive. None of the above.
Which of the following is true?
Curve $$ is increasing when curve $$ is positive. Curve $$ is increasing when curve $$ is positive. None of the above.
Which of the following is true?
Curve $$ is increasing when curve $$ is positive. Curve $$ is increasing when curve $$ is positive. None of the above.