The Total solution for NCERT class 6-12
Find points at which the tangent to thecurve y = x3 − 3x2 −9x + 7 is parallel to the x-axis.
The equation of the givencurve is
Now, the tangent is parallel to the x-axisif 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 isparallel to the x-axis are (3, −20) and
(−1, 12).