How about optimization problems such as this
I'll be taking pre-calc soon, and I've been wondering about something.
I know that some problems can be solved with algebra.
Tickets for a school play are $12 for adults and $8 for students. The school sold 200 tickets for Friday night. If the school earned $1,860 for the show, how many $12 tickets did they sell.
I can solve this example writing
12x + 8y = 1860
x + y = 200
(Can solve by elimination or substitution)
So, I was wondering if anyone could give me an example of a problem that cannot be solved by using only Algebra and must us Calculus to solve it.
The first problem in BAdhi's link can be solved without calculus. By AM-GM inequality, . Equality occurs if and only if x = 2y (x = 250, y = 125).
Other optimization problems don't have easy algebraic/geometric solutions and therefore must be solved using calculus. For example, find the area bounded by the x-axis and , .