The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. Year 0 3 6 9 12 15 Retail Sales 85.851 108.426 141.781 169.256 202.297 222.266 Let y be the retails sales in billions of dollars in x years since 1995. A linear model for the data is y=9.44x+84.182 A) Use the above scatter plot to decide whether the line of best fit, fits the data well. The function is a good model for the data. The function is not a good model for the data B) To the nearest billion, estimate the retails sales in the U. S. in 2011. billions of dollars. C) Use the equation to find the year in which retails sales will be $240 billion.
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.
The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995.
Year
0
3
6
9
12
15
Retail Sales
85.851
108.426
141.781
169.256
202.297
222.266
Let y be the retails sales in billions of dollars in x years since 1995. A linear model for the data is
y=9.44x+84.182
A) Use the above scatter plot to decide whether the line of best fit, fits the data well.
The
The function is not a good model for the data
B) To the nearest billion, estimate the retails sales in the U. S. in 2011. billions of dollars.
C) Use the equation to find the year in which retails sales will be $240 billion.
.
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