# How do you find the absolute maximum and absolute minimum values of f on the given interval: #f(x) = x-ln(3x) # on [0.5, 2]?

##### 1 Answer

Nov 28, 2016

abs min is at x=1, y= 1 - ln(3) abs max at x=2, y= 2- ln(6)

#### Explanation:

- need to differentiate to get critical point(s)
#dy/dx= 1 - 1/x# - therefore, critical point at x=1
- to left of x=1, dy/dx<0, and to the right it is >0.
- therefore, min at x=1.
- check endpoints to see which has largest y value; that occurs at x=2.