Analyzing a graph in exercise, analyze and sketch the graph of the function. label any relative extrema, points of inflection, and asymptotes.
y = in(x + 3)

analyzed & sketched

Step-by-step explanation:

We are given the function: y = In(x + 3)

So first we need to take the first derivative to find the interval of increase and decrease, then the second derivative to find the interval of concave up and concave down.

So it is always increasing function, and always concave down function.

Since it is a logarithmic function, x>3.

So, x = 3 is vertical asymptote.

I attached the sketch as a picture.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet