The equation of a curve is $y = x \ln x$. Find, respectively, the equations of the tangent and the

Question

The equation of a curve is $y = x \ln x$. Find, respectively, the equations of the tangent and the normal to the curve at the point where $x = e$. Hence find the area of the quadrilateral formed by the tangent and the normal to the curve at the point where $x = e$ and the axes.

Accepted Answer

(i) Tangent: $y=2x-\mathrm e$; normal: $y=-\dfrac12x+\dfrac{3\mathrm e}{2}$ (ii) $\mathrm e^2\text{ units}^2$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions

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