Question

Co-ordinates of a point on the curve y = x log x at which the normal is parallel to the line 2x – 2y = 3 are.

• A. (0, 0)
• B. (e, e)
• C. (e², 2e²)
• D. (e^–2, –2e^–2)

Answer 1

Answer: (D)

(e^–2, –2e^–2)

Answer 2

y = x log x

⇒ $\frac{dy}{dx} = 1 + \log x$

The slope of the normal = $- \frac{1}{\frac{dy}{dx}} = - \frac{1}{1 + \log x}$ & normal is parallel to 2x – 2y = 3

∴ $- \frac{1}{1 + \log x} = 1$

⇒ x = e ^{– 2}

∴ y = –2e ^{– 2}

∴ coordinate of point are $\left( e^{- 2}, - 2e^{- 2} \right)$