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Find points at which the tangent to the curve y = x3 − 3x2 − 9x + 7 is parallel to the x-axis.
Asked by Suresh Last Modified
Answer 
Harshit Bhardwaj
The equation of the given curve is
Now, the tangent is parallel to the x-axis if the slope of the tangent is zero.
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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