Re: Calculus problem example

How about optimization problems such as this

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 $\displaystyle f(x) = \sin {2x}$, $\displaystyle 0 \le x \le \pi$.