Answer
$f(x)=x^2+4$
Work Step by Step
This quadratic function has a negative derivative when $x<0$ and a positive derivative when $x>0$. Also at $x=0$ the derivative is 0.
To fulfill the requirement $f(0)=4$. We translated the graph up by 4 units. So the new graph is $f(x)=x^2+4$. This translation does not affect the derivative.
