quick question (1 Viewer)

[fullonoob]

The equation of the tangent to y=xlogx at x=e is y = 2x-e. Find the distance from this tangent to the origin

 

[Rezen]

perpendicular distance?

 

[alcalder]

The equation of the tangent to y=xlogx at x=e is y = 2x-e. Find the distance from this tangent to the origin

Perpendicular distance, IS the shortest distance.

Line perpendicular to y = 2x - e has the gradient -1/2.

It goes through (0,0) therefore has the equation
y =-x/2

These two lines cross at
-x/2 = 2x-e
-x = 4x - 2e
x = 2e/5
y = -e/5

distance = sqrt((-e/5)² + (2e/5)²)