Answer:
a = - 1.1
Step-by-step explanation:
The condition for a single variable function f(x) to be decreasing is f'(x) < 0.
f(x) = 4/x^2 - 6x + 9
Then, differentiating with respect to x on both sides we get,
f(x) = 4(-2)(1/x^3) - 6 < 0
-8/x^3 - 6 < 0
8/x^3 + 6 > 0
{Dividing both sides with - 1 and hence the inequality sign changes}
8/x^3 > -6
8 > - 6x³ {Multiplying both sides with x³}
6x³ > - 8 {Interchanging the sides}
x^3 > -8/6
⇒ x > - 1.1
So, a = - 1.1
