d. Find and discuss the meaning of any vertical asymptotes on the interval [0, 42]. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or I+ 1; z – 1). The order of the list does not matter. I = 0; 36 At the vertical asymptotes the comet is out of range of the laser
Minimization
In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.
Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.
Concavity
In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.
A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 36 days, is given by g(x)=200,000csc(π/36x).
Please answer (d).
![A laser rangefinder is locked on a comet approaching Earth. The distance g (r), in kilometers, of the
comet after æ days, for a in the interval 0 to 36 days, is given by g(z) = 200,000 csc (
36
a. Select the graph of g (x) on the interval [0, 42].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F128d7a0c-27a0-4083-8427-719d64466bab%2F38037095-8598-4d7b-8b3e-0dda4d8e3715%2Fw9ba5un_processed.jpeg&w=3840&q=75)
![b. Evaluate g (6).
Enter the exact answer.
g(6) = 400000
c. What is the minimum distance between the comet and Earth? When does this occur? To which
constant in the equation does this correspond?
The minimum distance between the comet and Earth is
200000
km which is the
stretching factor
.It occurs at 18
days.
d. Find and discuss the meaning of any vertical asymptotes on the interval [0, 42].
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or
x + 1; z – 1). The order of the list does not matter.
0; 36
At the vertical asymptotes the comet is
out of range of the laser.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F128d7a0c-27a0-4083-8427-719d64466bab%2F38037095-8598-4d7b-8b3e-0dda4d8e3715%2Fy2wh3ps_processed.jpeg&w=3840&q=75)
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