Applications-Of-Derivatives Question 462
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
Show Answer
Answer:
Correct Answer: D
Solution:
$ y=x^{3}-3x^{2}-9x+5 $
Þ $ \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 $
Þ $ x=-1,,3 $ .
BETA
