Question

What is the equation of the line tangent to `f(x)=ln(x^2+x)/(2x)` at `x=-1`?

Answer 1

The tangent at x = -1 doesn't exist.

Explanation:

Look at the function, `f(x) = ln(x^2+x)/(2x)`, it's not continuous, and it just so happens to not be differentiable at `x = -1`, because `ln((-1)^2-1) = ln(0)`, which is undefined.

Here's the graph:
graph{ln(x^2+x)/(2x) [-14.24, 14.24, -7.12, 7.12]}

You can see that the function is undefined at the point `P(-1,f(-1))`