What are the points of inflection of #f(x)=x^7/(4x-2) #?
Eliminating f' and f,
f''=0, for x satisfying
The second reduces to
Now, use the first three equations..
At x=0, all derivatives vanish.
At x=(35+-sqrt 217)/48#, f''' is not 0
So, the points of inflexion are .