Mark the correct alternative in the following:

If the function f(x) = kx^{3} – 9x^{2} + 9x + 3 is monotonically increasing in every interval, then

Formula:- (i) ax^{2}+bx+c>0 for all x a>0 and b^{2}-4ac<0

(ii) ax^{2}+bx+c<0 for all x a<0 and b^{2}-4ac<0

(iii) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on (a, b) is that f’(x)>0 for all x(a,b)

Given:-

f(x) = kx^{3} – 9x^{2} + 9x + 3

f’(x)=3kx^{2}-18x+9

for increasing function f’(x)>0

f’(x)>0

3kx^{2}-18x+9>0

kx^{2}-6x+3>0

using formula (i)

36-12k<0

k>3

1