Let f(x) = 6 - x^2. For 0 < w < root6, let A(w) be

[diedead]

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). Find A(1). For what value of w is A(w) a minimum?

 

[skeeter]

AP problem, huh?

tangent line has equation ...

y - (6 - w²) = -2w(x - w)

the line's x-intercept is where y = 0 ...
w² - 6 = -2w(x - w)
solve for the x-intercept in terms of w

the line's y-intercept is where x = 0 ...
y - (6 - w²) = -2w(-w)
solve for the y-intercept in terms of w

now, the area of the triangle is A = (1/2)(x-intercept)(y-intercept)

can you finish?