Question

what are the critical points for F(x) = -2*(x^2+1)/(x^2-1)^2

Answer 1

Agh. D: This one's messy.
Get some quotient rule & chain rule in there, take the derivative and set it equal to zero. Keep the -2 on the outside the whole time, for simplicity.

Answer 2

also find where f' doesnt exist

Answer 3

dy^2/d^2x -2/(x^2-1) = dy/dx(4x)/(x^2-1)
= (-12x^3-4)/(x^2 - 1)^3
set dy^2/d^2x to zero which equal

Answer 4

Ah yes, and the second derivative as well. Points of inflection. :P

Answer 5

wait oops.... i was look for the point of inflection sorry. So.....dy/dx -2/(x^2-1) = (4x)/(x^2-1)
set the derivative to zero and solve. the first derivative is 0.

Answer 6

there isn't a point of inflection because it is a monotonic function

Answer 7

You're correct, my bad. :P Got me confused for a second there.

Answer 8

complicated