7) Find points at which the tangent to the curve is parallel to the x-axis.
We are given :
Differentiating the equation with respect to x, we get :
It is given that tangent is parallel to the x-axis, so the slope of the tangent is equal to 0.
Thus, Either x = -1 or x = 3
When x = -1 we get y = 12 and if x =3 we get y = -20
So the required points are (-1, 12) and (3, -20).