JEE PYQ: Application Of Derivatives Question 44
Question 44 - 2020 (06 Sep Shift 2)
If the tangent to the curve $y = f(x) = x\log_e x$, $(x > 0)$ at a point $(c, f(c))$ is parallel to the line segment joining the points $(1, 0)$ and $(e, e)$, then $c$ is equal to:
(1) $\frac{e-1}{e}$
(2) $e^{1/(e-1)}$
(3) $e^{1/(1-e)}$
(4) $\frac{e}{e-1}$
Show Answer
Answer: (2)
Solution
$f’(c) = 1 + \ln c = \frac{e - 0}{e - 1} = \frac{e}{e-1}$. So $\ln c = \frac{e}{e-1} - 1 = \frac{1}{e-1}$. Hence $c = e^{1/(e-1)}$.
BETA
