Listen NCERT Audio Books to boost your productivity and retention power by 2X.
Mark the correct alternative in the following:
If the function f(x) = kx3 – 9x2 + 9x + 3 is monotonically increasing in every interval, then
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