#### Question

Find points at which the tangent to the curve *y* = *x*^{3} − 3*x*^{2} − 9*x* + 7 is parallel to the *x*-axis.

#### Solution

When *x* = 3, *y* = (3)^{3} − 3 (3)^{2} − 9 (3) + 7 = 27 − 27 − 27 + 7 = −20.

When *x* = −1, *y* = (−1)^{3} − 3 (−1)^{2} − 9 (−1) + 7 = −1 − 3 + 9 + 7 = 12.

Hence, the points at which the tangent is parallel to the *x*-axis are (3, −20) and

(−1, 12).

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Solution Find Points at Which the Tangent to the Curve Y = X3 − 3x2 − 9x + 7 is Parallel to the X-axis. Concept: Tangents and Normals.