# 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 :

or

or

It is given that tangent is parallel to the x-axis, so the slope of the tangent is equal to 0.

So,

or

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).

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