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  • The tangent to the curve represented by the y=x \ln x is required to have inclination with the

The tangent to the curve represented by the y=x \ln x is required to have 45^{\circ} inclination with the x-axis. The coordinates of the tangent point would be

Option: 1

(1,0)


Option: 2

(0,1)


Option: 3

(1,1)


Option: 4

(\sqrt{2},\sqrt{2})


Answers (1)

best_answer

Target is having inclination of 45^{\circ}with x-axis

\begin{aligned} &\mathrm{ \Rightarrow \quad \frac{d y}{d x}=\tan 45^{\circ} }\\ \\& \Rightarrow \quad \frac{\mathrm{d}(\mathrm{x} \ln \mathrm{x})}{\mathrm{dx}}=1 \\ \\& \mathrm{\Rightarrow \quad \ln x+\frac{x}{x}=1 \Rightarrow x=1} \\ & \end{aligned}

\mathrm{\therefore \text { At } x=1, y=1 \times l n^{\prime} 1=0 \text { so tangent point }=(1,0)}

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Rishi

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