I really need HELP with this problem, please please help?

Question

Let f(x) = (x + 1)^2/(x – 1)^3. The f “(x) = 2x^2 + 20x +26/(x – 1)^5. Over what intervals is the curve concave up?

a) x < -5 - 2√3 and -5 + 2√3 < x < 1
b) -5 -2√3 < x < -5 + 2√3 and x > 1
c) x > 1
d) -5 - 2√3 < x < -5 + 2√3

Answer 1

The function is concave up when f''(x) > 0.

The numerator of the function is positive when x is positive.
The denominator of the function is positive when (x-1) is positive since you are raising the term to an odd power.

x-1 >0 when x >1

f''(x) > 0 when x > 1

Your answer is C

Given a function if the slope of that function is positive, it is increasing (a positive slope has positive x for any positive y). Slope is determined by the first derivative.

If you look at that slope and you that the change in slope you will determine if the slope is increasing or decreasing, that is does the function point upward, or is it flattening out. This is concave up or concave down. It is determined using the second derivative.

Answer 2

c) x>1

Answer 3

i wonder if this is cheating? hmmmmmmm.........LOL, but really I don't know.....I mean who would?