Question

Function f(x) = 2x³ – 9x² + 12x + 29 is monotonically decreasing when

A. x < 2

B. x > 2

C. x > 3

D. 1 < x < 2

Answer 1

Correct answer is D.

Formula:-

(i) The necessary and sufficient condition for differentiable function defined on (a, b) to be strictly decreasing on (a, b) is that f’(x) < 0 for all x ∈ (a, b)

Given:-

for decreasing function f’(x) < 0

f’(x) < 0

\(\Rightarrow\) 6(x - 1)(x - 2) < 0

\(\Rightarrow\) 1 < x < 2