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

Jun 23, 2017

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

#### Explanation:

Look at the function, $f \left(x\right) = \ln \frac{{x}^{2} + x}{2 x}$, it's not continuous, and it just so happens to not be differentiable at $x = - 1$, because $\ln \left({\left(- 1\right)}^{2} - 1\right) = \ln \left(0\right)$, 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 $P \left(- 1 , f \left(- 1\right)\right)$