The tangent to the curve

at the point $P$ passes through the maximum point of the curve.

Find the coordinates of $P.$

Let $P$ have $x$ coordinate of $p.$ Find the tangent to the curve at the point

You know that $(-1,7)$ lies on the tangent, so you have a point to substitute into the equation of the tangent.

You should now have an equation in terms of $p$ only. It looks nasty, but it turns into an ok cubic.

The solutions, $p,$ to the cubic you found in hint $2$