A) \[x=0\]and 0
B) \[x=1\]and \[-1\]
C) \[~x=-1\] and 3
D) none of these
Correct Answer: C
Solution :
Equation of curve \[y={{x}^{3}}-3{{x}^{2}}-9x+5\] \[\frac{dy}{dx}=3{{x}^{2}}-6x-9\] We know that this equation gives the slope of the tangent to the curve, we also know that if the tangent is to the parallel to \[x-\]axis then\[\frac{dy}{dx}=0\] \[\Rightarrow \]\[3{{x}^{2}}-6x-9=0\] \[{{x}^{2}}-2x-3=0\] \[\Rightarrow \] \[x=-1,3\]
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