What are the points of inflection of f(x)=4 / (2x^2- 7x - 4?

$f ' \left(x\right) = \frac{- 16 x + 28}{2 {x}^{2} - 7 x - 4} ^ 2$
$f ' ' \left(x\right) = \frac{8 \left(12 {x}^{2} - 47 x + 57\right)}{2 {x}^{2} - 7 x - 4} ^ 3$
$f ' ' \left(x\right) = 0$ no values, $f ' ' \left(x\right)$ DNE at $x = 4 \mathmr{and} x = \left(- \frac{1}{2}\right)$
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 $x = 4 \mathmr{and} x = \left(- \frac{1}{2}\right)$