Finding the dimensions of the rectangle help?

Question

Find the dimensions of the rectangle of the largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.)

y = 7 - x²

Answer 1

Let (x, 7 - x²) is vertex in 1st quadrant. Then area Ax) = 2x(7 - x²) = 14x - 2x³;

A'(x) = 14 - 6x² = 0 x = √7/3; A''(x) = -12x; A''(√7/3) = -12√7/3 < 0. So, dimentions of rectangle: 2√7/3 and

7- 7/3 = 14/3

Answer 2