I'm working through some optimization questions and I got stuck, and ended up with the wrong answer. The question is:
There's a garden that needs to be enclosed, you have $60$m of fencing, one side is against a house so you need to enclose only three sides, maximize the area.
So what I did was,
Maximize area = $xy$
$$y = 60 - 2x$$ $$f(x) = x(60-2x)$$ $$= 60x-2x^2$$
$$f'(x) = 60-4x$$ $$= 4(15-x)$$
Now this is the part where I'm confused, I know that $y = 60-2x$, but how do I solve for $x$? I used $x = 15$, which gave me the wrong answer.