Answer:
Analyzed and Sketched.
Step-by-step explanation:
We are given [tex]y = x^2 \ln(\frac{x}{4})[/tex].
For sketching graph, we need to determine the following.
1) First derivative of y with respect to x to determine the interval where function increases and decreases.
2) Second derivative of y with respect to x to determine the interval where function is concave up and concave down.
[tex]y' = x + 2 x \ln(\frac{x}{4})[/tex]
[tex]x =4/\sqrt e[/tex] is absolute minimum.
[tex]y'' = 3 + 2\ln(\frac{x}{4})[/tex]
[tex]x = 4/e^{3/2}[/tex] is point where concavity changes from down to up.
Since it is logarithmic function, the graph covers right side of the x-axis and it cannot take the value pair (0,0)
The sketch is in attachment.
