Originally Posted by

**Adrian** Question: If they exist, find the horizontal and vertical tangent lines of the function f(x) = x(sqrt(4-x^2))

I think I found the x values at which the tangent lines are vertical and horizontal, but I'm not sure how to find the actual lines.

My solution (so far):

f'x = (4-x^2)^0.5 + (0.5x(4-x^2)^-0.5)*-2x

= ((4-x^2)^0.5)*((4-x^2)-x^2))

= (4-2x^2)/sqrt(4-x^2)

Horizontal tangent line is when numerator=0, therefore x= -sqrt2

Vertical tangent line is when denominator=0, therefore x= +/- 2

Anyway, I'm not sure if I'm going about the problem correctly.

Thanks