I'm not sure what rules I ought to use to solve this problem, and how I go about applying these rules. Since the problem involves a bounded area I am guessing it would involve integration. This is the problem:
For each x in the interval [0, 3], consider the triangle with vertices (0, 0), (x, 0) and (x, p(x)) where p(x) = 3 + 2x − x^2. Find the value of x which generates the triangle with the largest area.
If you could guide me through the solution that would be greatly appreciated.
Thanks in advance.