for every point (x,y) which is in the first quadrant and is on the graph
y = 24 -4x^2, consider the rectangle with corners (-x,0), (-x, y), (x,0) and (x,y).
for which value of x does the rectangle have maximal area?
Did you make a sketch?
base of rectangle = 2x , (from -x to +x)
height of rectangle = y
area = 2xy
= 2x(24-4x^2) = 48x - 8x^2
d(area)/dx = 48 - 16x = 0 for a max of area
16x=48
x=3