Triangle in Parabola Problem: A triangle is inscribed in the region bounded by the

Chapter 12, Problem 11

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Triangle in Parabola Problem: A triangle is inscribed in the region bounded by the parabola y = 9 x2 and the x-axis (Figure 12-3l). A vertex of the triangle is at the origin, and the opposite side is parallel to the x-axis. Another vertex touches the parabola at the sample point (x, y) in the first quadrant. Plot the area of the triangle as a function of x, and sketch the result. Find the value of x that maximizes the area of the triangle, and find the area of this maximal triangle. Figure 12-3 l