Question

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Answer 1

Answer:

  a = 3

Step-by-step explanation:

The function can be written as ...

  f(x) = 4/(x -3)^2

This has a vertical asymptote at x=3 and will be decreasing for all values of x to the right of that -- on the interval (3, ∞).

  a = 3

Answer 2

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