slope of line tangent to 1/x

Question

I am having difficulty understanding this, is the slope of a line tangent to 1/x never zero? or is this statement wrong?

Answer 1

That's correct, the derivative of 1/x is -1/x^2

Since x is in the denominator and therefore can't be 0 the slope of 1/x is always a negative number and simply undefined at x =0