1. ## Integral Word Problem

Hi,
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.

2. Originally Posted by ausar
Hi,
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.
$
A = \frac{1}{2} b \cdot h = \frac{1}{2} x \cdot \left(3 + 2x - x^2 \right)$

so find the max of $A$, i.e. $A' = 0$. Use the second derivative test to show it's a max.

3. Thank you very much for your response danny arrigo, however I am not quite sure as to what it is that I am doing wrong as I am still unable to arrive at the answer. Is it then possible that you may be able to explain further?
Also for what it may be worth, this particular question came with the graph seen below.`