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 = ln 5x/x^2

Answer 1

Answer:

Analyzed and Sketched.

Step-by-step explanation:

We are given $y=\frac{\ln\left(5x)}{x^2}$

To sketch the graph we need to find 2 components.

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.

$y'=\frac{1-2\ln\left(5x)}{x^3}=0$

$x = \sqrt e/5$ is absolute maximum

$y''=\frac{6\ln\left(5x)-5}{x^4}=0$

$x=e^{5/6}/5$ is the point concavity changes from down to up.

Here, x = 0 is vertical asymptote and y = 0 is horizontal asymptote.

The graph is given in the attachment.