What are the points of inflection of #f(x)=4 / (2x^2- 7x - 4#?
The numerator of the second derivative has no real roots, the only places where the second derivative is 0 or fails to exist come from the denominator. The second derivative fails to exist at at
These are the only points that could be points of inflection. You can only define them as points of inflection if curvature changes sign on either side of each value.