Analyzing a graph in exercise, analyze and sketch the graph of the function. label any relative extrema, points of inflection, and asymptotes.
f(x) = 1/xe^x

Analyzed & Sketched

Step-by-step explanation:

We are given the function:

So, we will find first derivative for finding the interval of increase and decrease.

it is increasing on (-∞, -1) and decreasing on (1,0) ∪ (0, ∞).

For concavity, we need to find the second derivative.

it is concave down on (-∞, 0) and concave up on (0, ∞).

x = 0 is vertical asymptote.

Sketch is given in the attachment.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

can i see the following ?

step-by-step explanation: