Let f : [0, 1] 
[0, 1] be the function defined by 
. Consider the square region S = [0, l]x[0,l]. Let G = {(x, y) 
S : y > f(x)} be called the green region and R = {(x, y) 
S : y < f(x)} be called the red region. Let L h = {(x, h) 
S : x 
[0, 1]} be the horizontal line drawn at a height h 
[0, 1]. Then which of the following statements is(are) ture?
such that the area of the green region above the line L h equals the area of the green region below the line L h
such that the area of the red region above the line L h equals the area of the red region below the line L h
such that the area of the green region above the line L h equals the area of the red region below the line L h
such that the area of the red region above the line L h equals the area of the green region below the line L h
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(b,c,d)
f'(x) = x 2 -2x + 
f'(x) = 0 at x= 
in [0,1]
A R = Area of Red region
A G = Area of Green region
Total area = 1
Correct when h = 
but 
is incorrect
Correct when h = 
is correct
When 
for some 
is correct
Option is remaining coloured part of option , hence option is also correct.
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