Question

Tangent to y = square root of x.
Does the tangent to the curve cross the x-axis at x = -1. If so, find an equation for the line and the point of the tangency. If not, why not?

Answer 1

The tangent is not crossing the x-axes, because:\[f=\sqrt{x}, f \prime=1/2\sqrt{x}, f \prime(-1)=1/2i \rightarrow equation of the tangent = y=(1/2i)x -(1/2i)\] from this it can be seen that the tangent is crossing Argon diagram at (-2/2i), when x=-1

If I'm wrong please do tell me where I'm wrong,