let the points of contact be (x,y) and (-x,y),
(there is symmetry in your parabola
Area of rectangle
= 2xy
= 2x(2 - x^2)
= 4x - 2x^3
differentiate, set the derivative equal to zero and solve for x
Easy from there.
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=2-x^2
What are the dimensions of such a rectangle with the greatest possible area?
Width=?
Height=?
2 answers
A cylinder is inscribed in a right circular cone of height 6.5 and radius (at the base) equal to 7.5 . What are the dimensions of such a cylinder which has maximum volume?