Question 328496
The max angle will be attained by the tangent line to the curve y=sqrt(x) that passes through x=-2.  The thing is, we have to find this point on the curve.

We can do this by using the equation of a line formula.

{{{y-y1=m(x-x1)}}}

y1=0, x1=-2, y=sqrt(x), m=1/(2*sqrt(x))

{{{sqrt(x)-0=1/(2*sqrt(x))*(x+2)}}}

Solving for x, we find x=2.

The line is tangent to the curve at (2,sqrt(2)).

By the law of tangents, we can easily find the angle now.

{{{arctan(sqrt(2)/4)=19.4712206345}}} degrees is the max angle.