Mark the correct A. –1 ≤ k < 1

B. k < –1 or k > 1

C. 0 < k < 1

D. –1 < k < 0

Formula:- (i) ax²+bx+c>0 for all x a>0 and b²-4ac<0

(ii) ax²+bx+c<0 for all x a<0 and b²-4ac<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) = x³ – 9k x² + 27x + 30

f’(x)=3x²-18kx+27

for increasing function f’(x)>0

3x²-18kx+27>0

x²-6kx+9>0

Using formula (i)

36k²-36>0

K²>1

Therefore –1 <k < 1