The function f(x)=2x3-9x2+12x-6 is monotonic decreasing, when
1<x<2
x>2
x<1
None of these
Explanation for correct option
Given function f(x)=2x3-9x2+12x-6
⇒f'(x)=6x2-18x+12
We know that the condition for f(x) to be monotonically decreasing is f'(x)<0.
⇒f'(x)<0⇒6x2-18x+12<0⇒x2-3x+2<0⇒x2-2x-x+2<0⇒x(x-2)-1(x-2)<0⇒(x-2)(x-1)<0⇒x∈1,2
Thus, f(x) decreases in the interval (1,2).
Hence, the correct option is A .
The interval on which the function f(x) = 2x3 + 9x2 + 12x - 1 is decreasing is (a) [-1, ∞) (b) [-2, -1] (c) (∞, -2] (d) [-1, 1]