Question

If the function f(x) = x³ – 9k x² + 27x + 30 is increasing on R, then

A. –1 ≤ k < 1

B. k < –1 or k > 1

C. 0 < k < 1

D. –1 < k < 0

Answer 1

Correct answer is A.

Formula:-

(i) ax² + bx + c > 0 for all x \(\Rightarrow\) a > 0 and b² - 4ac < 0

(ii) ax² + bx + c < 0 for all x \(\Rightarrow\) 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:-

for increasing function f’(x) > 0

Therefore –1 < k < 1