Question

Analyzing a Graph In Exercise, analyze and sketch the graph of the function. Lable any relative extrema, points of inflection, and asymptotes. See Example 6.

y = x^2 ln x/4

Answer 1

Analyzed and Sketched.

Explanation:

We are given
`y = x^2 \ln((x)/(4))`.

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.

`y' = x + 2 x \ln((x)/(4))`

`x =4/\sqrt e` is absolute minimum.

`y'' = 3 + 2\ln((x)/(4))`

`x = 4/e^(3/2)` 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.