Question

Suppose that f(x)=3x−6/x+5.

Use interval notation to indicate where f(x) is concave up or down.
Concave up:
Concave down:

Answer 1

What is the numerator and what is the denominator of this equation. There is too much ambiguity in your original written question:

(3x-6) / (x+5)
or
(3x-6)/(x) + 5
or
3x - (6)/(x+5)
or
3x - (6/x) +5

Answer 2

numerator: 3x-6
denominator: x+5

Answer 3

Reduce[D[(3 x - 6)/(x + 5), {x, 2}] > 0, x]

Answer 4

x < -5

Answer 5

pretty easy to see if you look at a plot

Answer 6

Can you put this in interval notation

Answer 7

(-Inf, -5)