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.

I'm confused the wording, but it seems to me like you take the derivative of f(x), find where it's zero, and then find where it changes from negative to positive. Or am I reading this completely wrong?

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pianogirl2422 wrote:I'm confused the wording, but it seems to me like you take the derivative of f(x), find where it's zero, and then find where it changes from negative to positive. Or am I reading this completely wrong?I figured it out, and it wasn't quite that simple. It really helps to understand it if you have the picture. A = bh/2, because this is just a triangle. It's like, the line tangent to 6 - x^2 at any point forms the hypotenuse of a triangle, with the axes as the legs. I figured it out to be when w = root2.