Q. 295.0( 1 Vote )

Mark the correct A. –1 ≤ k < 1

B. k < –1 or k > 1

C. 0 < k < 1

D. –1 < k < 0

Answer :

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

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