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Equation of Tangent at a Point (x,y) in Terms of f'(x)

If the tangen...

Question

If the tangent to the curve $y = x log x$ at $(c, f (x))$ is parallel to the line-segment joining $A (1, 0)$ and $B (e, e)$ , then c=...... .

\frac{e - 1}{e}

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log \frac{e - 1}{e}

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e^{\frac{1}{1 - e}}

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e^{\frac{1}{e - 1}}

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Solution

The correct option is D $e^{\frac{1}{e - 1}}$
slope of AB $= \frac{e}{e - 1}$
$\frac{d y}{d x} = 1 + log x$
slope at $(c, f (x))$
$1 + log c = \frac{e}{e - 1} ⟹ = e^{\frac{1}{e - 1}}$

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