Find the point p on the line yequals6x that is closest to the point left parenthesis 74 comma 0 right parenthesis. what is the least distance between p and left parenthesis 74 comma 0 right parenthesis

The least distance would be 73 units ( approx )

Step-by-step explanation:

Let the coordinates of P are ,

Since, point P lies on the line y = 6x

So, P will satisfy the above line,

,

Now, By the distance formula,

The distance between P and (74,0),

  ( From equation (1) )

Differentiating with respect to ,

Again differentiating with respect to x,

For maxima or minima,

,

At D''(x) = positive

Thus, for D is minimum,

And, minimum distance,