JEE Advance - Mathematics (1989 - No. 26)
Find all maxima and minima of the function
$$$y = x{\left( {x - 1} \right)^2},0 \le x \le 2$$$
Also determine the area bounded by the curve $$y = x{\left( {x - 1} \right)^2}$$,
the $$y$$-axis and the line $$y-2$$.
Also determine the area bounded by the curve $$y = x{\left( {x - 1} \right)^2}$$,
the $$y$$-axis and the line $$y-2$$.
The function has a minimum at x = 1/3 and a maximum at x = 1.
The area bounded by the curve, y-axis, and y=2 is 10/3 square units.
The function has a minimum at x = 1 and a maximum at x = 1/3.
The area bounded by the curve, y-axis, and y=2 can be found through integration.
The function has extrema only at the boundary values x=0 and x=2.