Question 827548
Between {{{x=-sqrt(5)}}} and {{{x=sqrt(5)}}}


Derivative of y=x^2+5 gives the formula for slope of any point on the parabola.
Slope formula or derivative for this is y'=2x, again, representing a slope of a line.


The line containing the origin and using that slope of 2x, would be {{{y=(2x)x+0}}} or simply {{{y=2x^2}}}.


Two lines must intersect:  The parabola, and that tangent line.
What is the x value for the intersection of these two equations?
{{{y=x^2+5}}} with {{{y=2x^2}}}...
'
{{{x^2+5=y=2x^2}}}
{{{5=x^2}}}
{{{x=-sqrt(5)}}} or {{{x=sqrt(5)}}}


The domain for this ability to touch the parabola from the orginin in without missing the parabola is {{{highlight(-sqrt(5)<=x<=sqrt(5))}}}