A) \[\left( \frac{3}{2},\frac{13}{2} \right)\]
B) \[\left( -\frac{5}{2},-\frac{17}{2} \right)\]
C) \[\left( \frac{3}{2},\frac{17}{2} \right)\]
D) \[(0,-4)\]
E) \[\left( \frac{3}{2},-\frac{17}{2} \right)\]
Correct Answer: E
Solution :
Tangent to any curve which is parallel to\[x-\]axis, if \[\left( \frac{dy}{dx} \right)=0\] Given \[y=2{{x}^{2}}-6x-4\] \[\Rightarrow \]\[\frac{dy}{dx}=4x-6=0\Rightarrow x=\frac{6}{4}=\frac{3}{2}\] \[\Rightarrow \]\[y=2.\frac{9}{4}-6.\frac{3}{2}-4\] \[=\frac{9}{2}-9-4=\frac{9-18-8}{2}=-\frac{17}{2}\] \[\therefore \]Required point is\[\left( \frac{3}{2},-\frac{17}{2} \right)\].
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