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

1 Answer
Jun 23, 2017

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))