How do you find the inflection points for #g(x)=-x^2+3x+4#?
Your function is a quadratic and is represented, graphically, by a parabola. The only point where your function changes slope or inclination is the vertex, BUT...the concavity does not change! You basically do not have inflection points (The parabola is always a downwards "U").
You can see this by evaluating the second derivative:
hope it helps,