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.

Assuming everyone in the family showers only once a day,time taken by 1 person to shower = 11*60+15= 675 secondstime taken by 5 people = 5*675 = 3,375 stime taken by the family in a week = 7*3,375 =23,625 samount of water used in a week = 23,625/(10*60) = 39.375 = 40 liters