Measuring Racial Prejudice, by Age Group 46 7 Key: <15: little or no bias 44 15-35: slight bias 42 42 35-65: moderate bias 40 38 Group Group 6 2 Group Group 1 36 35 3 Group 34 5 34- 33 Group 32 4 32- 31 30 29 28 26 Below 18-24 25-34 35-44 45-54 55-64 65+ 18 Age Range Score on the Implicit Association Test
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 bar graph shows the differences among age groups on the Implicit Association Test that measures levels of racial prejudice. Higher scores indicate stronger bias.
Solve, a. The data can be described by the following polynomial model of degree 3: S = 0.2x3 - 1.5x2 + 3.4x + 25 + (0.1x3 - 1.3x2 + 3.3x + 5). In this polynomial model, S represents the score on the Implicit Association Test for age group x. Simplify the model.
b. Use the simplified form of the model from part (a) to find the score on the Implicit Association Test for the group in the 45–54 age range. How well does the model describe the score displayed by the bar graph?
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