Question

An isosceles triangle has its vertex at the origin and its base parallel to the x-axis with the vertices above the axis on the curve y = 27-x^2. Find the largest area the triangle can have.

Answer 1

We are given with an isosceles triangle having a vertex on the curve given y =27-x^2 .
The area of the triangle, A= xy = x (27-x^2) 
A' = 27-x^2-2x^2 = 0 
x = 3 
Amax = 3(27-9) = 54 units2