You are about to erase your work on this activity. Are you sure you want to do this?
Updated Version Available
There is an updated version of this activity. If you update to the most recent version of this activity, then your current progress on this activity will be erased. Regardless, your record of completion will remain. How would you like to proceed?
Two young mathematicians witness the perils of drinking too much coffee.
Check out this dialogue between two calculus students (based on a true
Do you like coffee? I like coffee! Sometimes I feel really “bad,” sluggish
and tired. Then I drink coffee and I feel good! Sometimes I drink a lot of
But here’s the problem, see: If I drink too much, I become over excited
and can’t stop talking. I just drink coffee, then talk. Then drink more
coffee. Then I start to feel sick. Ugh. I have a love-hate relationship with
If only there were a calculus solution to this problem!
Remember, calculus is about studying functions. If we can “see” a function in the
work above, maybe we can figure out how to solve it.
If we were to try to solve Devyn’s coffee problem, what would be the best function
How many donuts Devyn eats.How “good” Devyn feels after cups of
coffee.How many cups of coffee Devyn drinks when Devyn feels “good.”Impossible to say.
If we let be “How ‘good’ Devyn feels after cups of coffee,” and we think about what
Devyn says above, is there an amount Devyn can drink and feel maximally “good?”
“Yes” is probably the best answer, though we are assuming that Devyn feels “bad”
without enough coffee, “good” with some, and “bad” again with the function
continuously growing and then decreasing.