Question

Minimum distance between the curves $f(x)=e^x$ and $g(x)=\ln x$ is

• A. $\sqrt{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. 1
• D. $2(\sqrt{2}-1)$

Answer 1

Answer: (A)

Minimum distance is the distance along the common normal to both the curves i.e. $y=$ $x$ must be parallel to the tangent as both the curves are inverse of each other.
$\frac{ dy }{ dx }|_{ x _1}= e ^{ x _1}=1 $
$ \Rightarrow x _1=0 \text { and } y _1=1 $
$\therefore AB =\sqrt{2} $