Question

The point on the curve $ y=2{{x}^{2}}-6x-4 $ at which the tangent is parallel to the $ x- $ axis, is:

• 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) $

Answer 1

Answer: (E)

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) $ .