Determine the minimal distance from point (-3,3) to the curve given by y= (x -3)^3

Question

Determine the minimal distance from point (-3,3) to the curve given by y= (x -3)³

Answer 1

The shortest distance is on the perpendicular to the curve.

1) determine the slope of the tangent to the curve - first derivative.

2) take the negative reciprocal, this is the slope of the normal - perpendicular

3) determine equation of normal passing through the given point

4) determine the point of intersection of the normal and the curve.

5) use distance formula to determine distance from point to the curve.