Question

Is there a point of oblique inflection at y=x^3 + 4x^2-9

Please show your working.

Answer 1

\[\huge y=x^3 + 4x^2-9\]
\[\huge \frac{dy}{dx}=3x^2+8x\]
\[\huge \frac{d^2y}{dx^2}=6x+8\]
At IP's (Inflection/Inflexion Points)
\[\large \frac{d^2y}{dx^2}=0\]
\[\huge 6x=-8\]
\[\huge x=-\frac{4}{3}\]
\[\huge y=-\frac{115}{27}\]