Applications Of Derivatives Question 134
Question: The abscissae of the points, where the tangent to curve $ y=x^{3}-3x^{2}-9x+5 $ is parallel to x-axis, are
[Karnataka CET 2001]
Options:
A) 0 and 0
B) x = 1 and - 1
C) x = 1 and - 3
D) x = - 1 and 3
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Answer:
Correct Answer: D
Solution:
$ y=x^{3}-3x^{2}-9x+5 $
therefore $ \frac{dy}{dx}=3x^{2}-6x-9. $
We know that this equation gives the slope of the tangent to the curve. The tangent is to parallel to x-axis,
$ \therefore $ $ \frac{dy}{dx}=0 $ . Therefore $ 3x^{2}-6x-9=0 $
therefore $ x=-1,,3 $ .
BETA
