Question

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

y = 8 In x/x^2

Answer 1

Analyzed ans Sketched.

Explanation:

We are given the function:

`y = 8 \ln (x)/x^2`

The first derivative of y:

`y' = (8x-16x\ln(x))/(x^4) =(8-16\ln(x))/(x^3) =0`

The root
`x = \sqrt e` is absolute maximum.

The second derivative of y:

`y''=(-16x^2-24x^2+48x^2\ln(x))/(x^6) =(48\ln(x)-40)/(x^4) =0`

The root
`x = e^(5/6)` is point where concavity changes from down to up.

x = 0 is vertical asymptote.

y = 0 is horizontal asymptote.

The sketch is given in the attachment.