Find the smallest integer value of $c$ such that the function $f(x)=\frac{2x^2+x+5}{x^2+4x+c+12x+x^2}$ has a domain of all real numbers.
Simplify the denominator to
2x^2 + 16x + c
We need the discriminant of this to be < 0 (so that the denominator has no real 0's )
16^2 - 4(2)c < 0
256 - 8c < 0
256 < 8c
32 < c
33 is the smallest integer
+1348 
