Question

The tangent to the curve represented by y = x log x is required to have 45° inclination with the x axis. The coordinates of the tangent point would be
1. (1, 0)
2. (0, 1)
3. (1, 1)
4. \(\left( {\sqrt 2 ,\;\sqrt 2 } \right)\)

Answer 1

Correct Answer - Option 1 : (1, 0)

Target is having inclination of 45° with x-axis

\(\begin{array}{l} \Rightarrow \frac{{dy}}{{dx}} = \tan 45^\circ \\ \Rightarrow \frac{{d\left( {xln\;x} \right)}}{{dx}} = 1\\ \Rightarrow \ln x + \frac{x}{x} = 1 \end{array}\)

∴ At x = 1, y = 1 × ln1 = 0