Question

Find the point P on the parabola y=x^2 closest to the point (3,0).

Answer 1

if we take square root (x - 3)^2 + y^2
y = x^2
(x - 3)^2 + x^4
f(x) = x^4 + x^2 - 6x + 9.
first derivation:
f'(x) = 4x^3 + 2x - 6.
4x^3 + 2x - 6 = 0.
one solution is x = 1
second derivation
f"(x) = 12x^2 + 2
it is positive for x = 1
hope it helps