Mark the correct alternative in the following:
If the function f(x) = x³ – 9k x² + 27x + 30 is increasing on R, then

Question

Mark the correct alternative in the following: If the function f(x) = x 3 – 9k x 2 + 27x + 30 is increasing on R, then

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) = 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

Mark the correct alternative in the following:If the function f(x) = x3 – 9k x2 + 27x + 30 is increasing on R, then

Mark the correct alternative in the following:
If the function f(x) = x³ – 9k x² + 27x + 30 is increasing on R, then