Question

How do you find the points of inflection of the curve `y= \frac { x ^ { 3} } { a ^ { 2} + x ^ { 2} }`?

Answer 1

`x_1=0` or `x_2=sqrt(3)a` or `x_3=-sqrt(3)a`

Explanation:

Differentiatin by the quotient rule we get
`y'=(x^2(3a^2+x^2))/(a^2+x^2)^2`
and once more
`y''=(2xa^2(3a^2-x^2))/(a^2+x^2)^3`
Solving `y''(x)=0` you get the solutions above.