Saturday

October 25, 2014

October 25, 2014

Posted by **Help asap!! plz** on Friday, October 22, 2010 at 6:11pm.

f(x) = x/(x^2 + 2)

(a) Determine the intervals on which the function is concave up. Enter the leftmost interval first (e.g. (1,2) would come before (3,4)).

(b) Determine the intervals on which the function is concave down. Enter the leftmost interval first.

i only got to figure out the first derivative. And i did figure out second derivative but it came out to be some thing very long and nasty. so please help!

f'(x)=((x^2+2)-2x)/(x^2 + 2)^2

- CALCULUS -
**Reiny**, Friday, October 22, 2010 at 6:24pmalways simplify your first derivative before trying to take the second deriv.

I had it as

f' (x) = (2-x^2)/(x^2 + 2)^2

f'' (x) =[ (x^2+2)^2(-2x) - (2-x^2)(2)(x^2=2)(2x)]/ (x^2+2)^4

this factored to

-2x(x^2+2)[x^2+2 + 2(2-x^2)]/(x^2+2)^4

= -2x(6-x^2)/(x^2+2)^3

now the denominator cannot be zero and will always be positive, so as far as signs are concerned, we could ignore it.

so the curve is concave up when

-2x(6-x^2) > 0 or

2x(6-x^2) < 0

and the curve is concave down when

-2x(6-x^2) < 0 or

2x(6-x^2) > 0

can you take it from there?

btw, the points of inflection happen when

x = 0 or x = ±√6

**Answer this Question**

**Related Questions**

calc - Consider the function below. (Round the answers to three decimal places. ...

Calc - f(x) = x^2 / (x - 7)^2 (a) Find the vertical and horizontal asymptotes. x...

math (calculus) PLZZZ help! - Consider the function below. (Round the answers to...

calculus - Given f(x)=sin(x)-2cos(x) on the interval [0,2pi]. a) Determine where...

calculus help - Produce graphs of f that reveal all the important aspects of the...

Calculus - Suppose you know that f(x) is an odd functon on the domain of all ...

calculus - For x including [–15, 13] the function f is defined by f(x)=x^7(x+4)^...

math-calc - Consider the function f(x)= (2x+8)/(6x+3). For this function there ...

Math - Consider the equation below. (Give your answers correct to two decimal ...

Calculus - THANK YOU TUTORS SO MUCH FOR YOUR HELP Determine the intervals on ...