The minimum distance between a point on the curve `y = e^x` and a point on the curve `y=log_e x` is

Options

A. `(1)/(sqrt2)`
B. `sqrt2`
C. 3
D. `2sqrt2`

Answer

B

Explanation

Since `y=e^(x) and y=log_(e)x` are inverse to each other their graphs are symmetrical about `y=x`.
Minimum distance between the curves is the distance between the points on the curves where tangent is paralled y = x or slope of tangent is 1.
Now for `y=e^(x),y^(x)` for `e^(x)=1, x=0,` so the point on the cure `y=e^(x)` is `(0,1)` and symmetric point on the curve `y=log_(ex)` is (1).
Distance between these point is `sqrt2.`