Max rectangle under a parabola

MediumCalculus~6m

A rectangle has its base on the xx-axis and its two top corners on the parabola y=1−x2y = 1 - x^2. What is its maximum possible area? (to 3 decimals)

Show hints (2)+
  1. Parametrize by the corner's xx; area =2x(1−x2)=2x(1-x^2).
  2. Maximize, then plug x=1/3x=1/\sqrt3 back in.

Answer

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0.77 (± 0.005)

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