Question

What point on the curve y = √ x is closest to the point (5, 0)?

Answer 1

for a given (x,√x) on the curve, its distance to (5,0) can be calculated by pythagoras as:

D = √((5-x)² + √x²) = √(x²-9x+25)

We have to find the lowest D. To calculate that, we can find the minimum of x²-9x+25 which is at 9/2 (remember the -b/2a formula).

So the distance is minimal at the point (9/2, 3/√2)