Use the First Derivative Test to determine whether the critical point is a local min or max (or neither). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x)=(ln(2x)/8x)-7 (x>0)

Also determine the intervals on which the function is increasing or decreasing.

Step-by-step explanation:

Let be , the first and second derivatives of the function are, respectively:

Now, let equalise the first derivative to zero and solve the resulting expression:

This result is evaluated at the second derivative expression:

The critical value leads to a critical maximum and there are two intervals:

- Increasing

- Decreasing

The graphic of the function is presented below as attachment.

45.3592

step-by-step explanation: