What is the largest rectangle that can be inscribed in the first quadrant of the ellipse
I let x and y equal 0 to find the intercepts, but that does not lead to the solution.
1. Draw a sketch.
2. Let l denote the length of the rectangle and w the width. Then the area of the rectangle is:
3. Plug in l instead of x and calculate the y-value which is the width of the rectangle:
4. You now got the area as a function in l:
5. Differentiate a wrt l and solve the equation a'(l) = 0 for l. I've got
6. Now calculate the maxium area.