Question

Let f(x)=x^2+x+14. What is the value of f(x) for which the tangent line to the graph of y=f(x) is parallel to the x-axis?

Answer 1

the first derivative must be 0 there, for such thing to occur.
for ax^2+bx+c, -b/2a=0
for your case
f'(x)=2x+1
2x+1=0
x=-1/2

Answer 2

That's the same answer I got but when I enter it into my homework it says it's incorrect