Really need help

[lucky_luke]

hi

What point on parabola y = x^2 - 3x + 3 is closest to origin O ( point T(0, 0) )?

y^2 = (x^2 - 3x + 3)^2

D - distance from point P(x, y) on parabola to T(0, 0)

D^2 = g(x) = x^2 + y^2 = (x^2 - 3x + 3)^2 + x^2

g'(x) = 12x^2 - 36x + 32

Local minimum of g'(x) should be the answer, but there aren't any solutions for x
when 12x^2 - 36x + 32 = 0, at least not for x being real number. What am I doing wrong?

thank you

 

[tkhunny]

Your derivative is whacked. Please show how you achieved your result.

Ignoring the last term for a moment:

(d/dx)(x^2 - 3x + 3)^2 = 2*(x^2 - 3x + 3)*(3x-3)

That's a cubic. How did you manage only quadratic?