Science:Math Exam Resources/Courses/MATH104/December 2011/Question 01 (g)/Solution 1
The given function is increasing where its first derivative is positive. Taking the derivative yields
We must now solve the inequality for x yields the interval where ƒ is increasing. We will only be interested in positive values of x, as negative values of x are not in the domain of the given function (because of the natural logarithm). Therefore,
Therefore, we have
The negative solution was ruled out because of the requirement that x be a positive number.
The interval on which ƒ is increasing is