Question

What is the slope of the tangent line of `x^2 + y^2 = 1/2` at `x=1`?

Answer 1

There is no point on the graph with `x=1`, so there is no tangent line at `x=1`.

Explanation:

For `x^2+y^2=1/2`, if `x=1`, then `y^2 = -1/2`.
There is no real `y` that solves this.

Geometrically

The graph of `x^2+y^2 = 1/2` is a circle of radius `sqrt2/2`.

The maximum `x` value on that circle is `x=sqrt2/2 ~~ 0.7071`.