Question

How do you determine whether the function `y=ln x` is concave up or concave down and its intervals?

Answer 1

The graph of `y = lnx` is concave down on `(0,oo)`.

Explanation:

The domain of `lnx` is `(0,oo)`.

The second derivative is : `-1/x^2` which is always negative.

So the graph of `y = lnx` is concave down on `(0,oo)`.