A) \[x=1\]and -1
B) \[x=1\] and 3
C) \[x=1\] and -3
D) \[x=0\]and 0
Correct Answer: B
Solution :
Given, \[y={{x}^{3}}-3{{x}^{2}}-9x+5\] On differentiating both sides w.r.t. x, we get \[\frac{dy}{dx}=3{{x}^{2}}-6x-9\] We know that, this equation gives the slope of the tangent to the curve. But we are given that tangent is parallel to X-axis. \[\therefore \] \[\frac{dy}{dx}=0\] \[\Rightarrow \] \[3{{x}^{2}}-6x-9=0\] \[\Rightarrow \] \[3(x+1)(x-3)=0\] \[x=-1,3\]You need to login to perform this action.
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