Q. 165.0( 1 Vote )

Mark the correct A. k < 3

B. k ≤ 3

C. k > 3

D. k < 3

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) = kx3 – 9x2 + 9x + 3


f’(x)=3kx2-18x+9


for increasing function f’(x)>0


f’(x)>0


3kx2-18x+9>0


kx2-6x+3>0


using formula (i)


36-12k<0


k>3

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