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

Question

Philoid · Accepted 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

Mark the correct alternative in the following:If the function f(x) = kx3 – 9x2 + 9x + 3 is monotonically increasing in every interval, then

Mark the correct alternative in the following:
If the function f(x) = kx³ – 9x² + 9x + 3 is monotonically increasing in every interval, then