1. ## Calculus problem example

I'll be taking pre-calc soon, and I've been wondering about something.

I know that some problems can be solved with algebra.

Example:

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.

2. ## Re: Calculus problem example

How about optimization problems such as this

3. ## Re: Calculus problem example

The first problem in BAdhi's link can be solved without calculus. By AM-GM inequality, $\displaystyle \frac{x + 2y}{2} \ge \sqrt{2xy} \Rightarrow \frac{500}{2} \ge \sqrt{2xy}$. 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 $\displaystyle f(x) = \sin {2x}$, $\displaystyle 0 \le x \le \pi$.