The table below shows the amounts of crude oil (in thousands of barrels per day) produced by a country and the amounts of crude oil (in thousands of barrels per day) imported by a country, for the last seven years. Construct and interpret a 98% prediction interval for the amount of crude oil imported by the this country when the amount of crude oil produced by the country is 5,583 thousand barrels per day. The equation of the regression line is y = - 1.116x + 15,810.670. Oil produced, x Oil imported, y 5,773 5,694 5,638 5,481 5,165 5,051 5,010 9,345 9,132 9,616 10,049 10,152 10,165 10,030 Construct and interpret a 98% prediction interval for the amount of crude oil imported when the amount of crude oil produced by the country is 5,583 thousand barrels per day. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest cent as needed.) O A. There is a 98% chance that the predicted amount of oil imported is between and thousand barrels, when there are 5,583 thousand barrels produced. O B. We can be 98% confident that when the amount of oil produced is 5,583 thousand barrels, the amount of oil imported will be between and
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.
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