A function and its second derivative are given. Determine the concavity of $f$ and find $x-$values where points of inflection occur.

$f(x)=\frac{x^2+25x+140}{x^2+24x+144},f^{\text{'}\text{'}}(x)=\frac{2x-72}{(x+12{)}^4}$

Determine the concavity of f $.$ Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A$.$ The curve is concave down on $$ and concave up on $$

$($Type your answers in interval notation.$)$

B$.$ The curve is concave up for all real numbers.

C$.$ The curve is concave down for all real numbers.