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sveticcg [70]
3 years ago
13

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?

Mathematics
2 answers:
qaws [65]3 years ago
8 0

Answer:

Just did this. The answer is 3

Step-by-step explanation:

harkovskaia [24]3 years ago
5 0

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)

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