This is the 1994 free-response question for BC.
Let f(x) = 6 - x^2. For 0 < w < root6, let A(w) be the area of the triangle formed by the coordinate axes and the line tangent to the graph of f at the point (w, 6-w^2). There is a graph with it.
(A) Find A(1).
I did this, it wasn't hard. Answer of 49/4 u^2.
(b) For what value of w is A(w) a minimum?
This is the one I'm stuck on. I'm pretty sure it involves the second fundamental theorem. I'm really, really stuck. I could do it if I understood how to set up the area function. A will equal the integral of something, but I don't know how to come up with a general term for the function that is the hypotenuse.