I am trying to find the minimum and maximum distance between point (0,4) and the line y=(x^2)/4 in the region of 0<=x<=2√3.

This is what i have so far

y(distance)=√((x-0)^2+((x^2)/4)^2)

=(x^2+(X^4)/16+16)^0.5

then calculate y'

then make y'=0

then determine if max or min using 2nd derivative test

The problem i am having is that the answers i get for x when y' = 0 are imaginary. i have computed this problem using matlab and get the same answers except that they are real and have isolated the problem to my simplification of y.

matlab gives it as y=0.25(-16x^2+x^4+256)^0.5

Could some one please explain how to simplify y=(x^2+(X^4)/16+16)^0.5 to y=0.25(-16x^2+x^4+256)^0.5 or suggest a better way to approach this problem

Thanks in advance