Calculus Points of Inflection?

Question

The original equation is (x^2+1)/(x+1). I found my second derivitive to be (4x-4)/ (x^4+4x^3+6x^2+4x+1). I need to find the points of inflection. I realize that these are found when the second derivitive is equal to zero. Am I correct in assuming that this function has no points of inflection.

Answer 1

(x²+1)/(x+1).
f(x) = x²+1, g(x) = x+1
[ 2x*(x+1) - x² * 1 ] / (x+1)²
(2x²+2x - x²) / (x+1)²
x²+2x / (x+1)²

f(x) = x²+2x, g(x) = (x+1)²
(( [ (2x+2)*(x+1)² ] - [ x²+2x * 2(x+1) * 1 ] )) / ((x+1)²)²
[ (2x+2)(x²+2x+1) - (x²+2x)(2x+2) ] / (x+1)^4
[ 2x³+4x²+2x+2x²+4x+2 - (2x³+2x²+4x²+4x) ] / ((x+1)²)²
[ 2x³+4x²+2x+2x²+4x+2-2x³-2x²-4x²-4x) ] / ((x+1)²)²
[ 2x+4x+2-4x) ] / ((x+1)²)²
(2x+2) / ((x+1)²)²
2(x+1) / (x+1)^4
2 / (x+1)^3 <----dy²/dx² Yours was incorrect.

And yes, this will never have an inflection point. It will only approach y=0 as x approaches +/- ∞ and approach x=0 as x approaches 0

Answer 2

i've got only are available the time of this question, which looked vaguely exciting. I did what the different answerers did - looked for table sure factors by differentiating the function given y = x + (x - 8)^(2/3) dy/dx = a million + (2/3).(x - 8)^(-a million/3) which indicated a single table sure element at x = 8 - (2/3)^3 = 7.704. the 2nd differential d^2y/dx^2 = - (2/9).(x - 8)^(-4/3) indicated that this became right into a optimum. even with the undeniable fact that, this gave upward push to a difficulty: at super destructive values of x, y will strengthen gradually in the direction of the optimum at x = 7.704. At super beneficial values of x, the slope is likewise beneficial, with y increasing gradually. So on the initiating sight there might desire to be a minimum above x = 7.704 to ensure that the slope to return to a favorable fee. yet there is not any sign of it utilizing the approaches above. Then, observing the expressions above, I realised that there is a 2nd severe element, even with the undeniable fact that that's no longer a minimum or table sure element. the two the 1st and 2nd derivatives (and definitely all greater derivatives) are actually not defined at x = 8 ie there are discontinuities there (yet no longer contained in the function itself). So the finished answer is that there is a shallow optimum table sure element at x = 7.704, and a 2nd severe element at x = 8 the place the derivatives are actually not defined..

Answer 3

why don't you figure out for yourself if its correct. For your information, I'm asking people to help me with my physics questions because I take a very difficult course that I'm sure you know nothing about. I ask people my homework questions to help me grasp the concept of them because there are many repeats on the tests and I need help understanding them. So don't make assumptions when you know nothing about the questions that i'm asking and the course that I'm taking!!!

Answer 4

f''(x)=0
x=1
find f'''(x) and for x=1 if it is not zero thenx=1 is a point of inlexion