Respuesta :

Answer:

Analyzed ans Sketched.

Step-by-step explanation:

We are given the function:

[tex]y = 8 \ln (x)/x^2[/tex]

The first derivative of y:

[tex]y' = \frac{8x-16x\ln(x)}{x^4} =\frac{8-16\ln(x)}{x^3} =0[/tex]

The root [tex]x = \sqrt e[/tex] is absolute maximum.

The second derivative of y:

[tex]y''=\frac{-16x^2-24x^2+48x^2\ln(x)}{x^6} =\frac{48\ln(x)-40}{x^4} =0[/tex]

The root [tex]x = e^{5/6}[/tex]  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.

Ver imagen erturkmemmedli