Question

If the interval (a, ∞) describes all values of x for which the graph of 4/x^2-6x+9 is decreasing, what is the value of a?

Answer 1

Answer:

a = - 1.1

Step-by-step explanation:

Condition for a single variable function f(x) to be decreasing is f'(x) < 0.

So, in our case, $f(x) = \frac{4}{x^{2}} - 6x + 9$.

Then, differentiating with respect to x on both sides we get,

$f'(x) = 4(- 2)\frac{1}{x^{3}} - 6 < 0$

⇒ $- \frac{8}{x^{3}} - 6 < 0$

⇒ $\frac{8}{x^{3}} + 6 > 0$

{Dividing both sides with - 1 and hence the inequality sign changes}

⇒ $\frac{8}{x^{3}} > - 6$

⇒ 8 > - 6x³ {Multiplying both sides with x³}

⇒ 6x³ > - 8 {Interchanging the sides}

⇒ $x^{3} > - \frac{8}{6}$

⇒ x > - 1.1

Therefore, a = - 1.1. (Answer)

Answer 2

Answer:

Just did this. The answer is 3

Step-by-step explanation: