Question

Find any relative extrema and inflection points of the function. Use a graphing utility to confirm your results
y= x ln x

Answer 1

find dy/dx..set that equal to 0 for points of inflection or maximas/minimas..

Answer 2

Using the product rule, you have:

(x)(ln x)' + (ln x)(x)' = 1 + ln x = y'

So, y' = 0 at e^(-1) So, that is your minimum, and the function is defined for x > 0.

The second derivative is 1/x so the whole graph is concave up. Graph attached.

Answer 3

Thank you. I appreciate it!

Answer 4

You're welcome!