Question

how would you do this question A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 10-x^2. What are the dimensions of such a rectangle with the greatest possible area?

Answer 1

\[A(x)=(base)(height)=2xy=2x(10-x^2)=20x-2x^3\]maximize A(x) by setting A'(x)=0, then plug that value of x back into A(x) to find the maximum area.