1h(x)=f(x)-(f(x))2+(f(x))3
h'(x)=f'(x)-2f(x)f'(x)+3f(x)2f'(x)
=f'(x)[1-2f(x)+3f(x)2]
Discriminant of the bracket = 4-4x3
=-8
Since a>0 and D<0 for all values of x therefore the contents of the bracket is always positive
therefore
h'(x) = f'(x) x [+ve no]
therefore h'(x) is depends on the value of f'(x)
i.e. if f(x) is increasing(f(x)>0) then h'(x) is increasing
and similarly for decreasing............
therefore (a) and (c) is the ans
hope dis helps u........
