Determine maximum value of this solution for t>0

[NINHARDCOREFAN]

The equation is y=e^(-t)-e^(2t)

It says: Determine maximum value of this solution for t>0 and the value of t where this maximum occurs.

Doesn't the maximum occur at 0? So what is the question asking?

 

[quantumdude]

Doesn't the maximum occur at 0?

Yes.

So what is the question asking?

If I were asking the question, I would expect my students to show that zero is a critical number of f(x), and then to use either the first or second derivative test to demonstrate that there is indeed a maximum at that point.