I really need HELP with this question, 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

Hmmmm......
How many accounts do you have?

Spring S
http://answers.yahoo.com/my/profile;_ylt=Aq_L_9xw4kEaft1g7V.5ZnMjzKIX?show=AR3yuR0oaa

Model Beauty
http://answers.yahoo.com/my/profile;_ylt=Ao3xc1h5a2NzHmxvERv4LWsjzKIX?show=zT73fINYaa

Brit L
http://answers.yahoo.com/my/profile;_ylt=AstOoV6ywt_EL5Mvc4P7cuUjzKIX?show=GlH9Vichaa

slow_math
http://sg.answers.yahoo.com/my/profile;_ylt=Avbv2W_0ac7XlZD_deaVv9QjzKIX?show=bb6fc83042b0cf90462c8a2bc9680654aa

mark P
http://answers.yahoo.com/my/profile;_ylt=AlkcZx.arZnCKSe9BWPhKJPty6IX?show=qbKNbQeraa

Full of Questions
http://answers.yahoo.com/my/profile;_ylt=Ai91AxxL5Sw.NBn9QJTRL6Lty6IX?show=xt6lFi7Iaa

Ash O
http://answers.yahoo.com/my/profile;_ylt=AuMBUUEiBk9TfaRMEG5XHaQCxgt.?show=8SYIUURMaa

That's at least 7.

It doesn't take a rocket scientist to figure this out.
All the questions are pretty much posed the same way, AND some of the questions are repeated by the multiple accounts.

Answer 2

Setting f''(x) = 0 gives
x^2 + 10x + 13 = 0
Using the quadratic formula gives
x = -5 +/- 2 sqrt(3)
Draw a number line with these two points and x = 1.
On the first interval, try f''(-10) = (200 -200 +26)/(-11)^5 < 0.
Draw a "hill" in this interval, since f is concave down.
On the 2nd interval, try f''(-5) = ( 2(25) -100 + 26) / (-6)^5 > 0.
Draw a "U" in this interval, since f is concave up.
On the 3rd interval, try f''(0) = 26/(-1)^5 < 0.
So f is concave down in this interval.
On the last interval, try f''(10) = (200+200+26) / (9)^5 > 0.
So f is concave up in this interval.

Answer: b)

BTW, are you sure you typed in the right formulas for f(x) and f''(x). I tried to get f''(x) from f(x), but I got a different f''(x). Or maybe I'm just tired. :)

Answer 3

You can write the second derivative as

f´´(x) = 2(x^2 +10x+13)/(x-1)^5

Now you find the roots and discontinuities of the second derivative, that are x = -5+2sqrt(3), x= -5 - 2sqrt(3) and x=-1

Studying the second derivative signals you will find that it is
negative for -5 -sqrt(3)1

And this are the intervals where the curve is concave up.

Attention: it is the union of two intervals... so you must use the connective OR , not AND as written in b)

Answer 4

let´s factorize the numerator of f´´

x^2+10x+13=0 so x=((-10+-sqrt(100-52))/2
x= -5+- 2sqrt3

The sign of f´´ is --------(-5-2sqrt3)+++++(-5+2sqrt3)----- 1+++++so the answer is b)