Hi all! I'm new to the forums. I'm finishing up high school calculus and was looking for some help with a question.
I was asked to find the regions of increase and decrease for y=xln(x^2)
First, I found the derivative to be 2(1+lnx)
Next, to find when the function is increasing, I had to solve for lnx>-1
Then I went x>e^-1, so x>1/e
This suggests to me that the function is increasing beyond x=1/e. While this is true, when I graphed the initial function, it appears as if the graph changes directions twice, whereas I only found it to change direction once.
Could someone please indicate where my error is? Thank you!