The function f(x) = - 7.57 In x + 61 models the percentage of first-year college men in a certain country expressing antifeminist views (by agreeing with the statement) x years after 1969. Complete parts (a)-(b). Statement: "The activities of a married woman are best confined to the home and family." Opposition to Feminism among First-Year College Students, 1970-2004 70- 61.8 60- 45.7 50- 36.2 33.7 32.8 40- 30- 20- 10- 33.3 18.2 18.1 16.8 15.8 Men Women 0- 1970 1980 1990 2000 2004 a. Use the function to find the percentage of first-year college men expressing antifeminist views in 2004. Does this function overestimate or underestimate the percentage displayed on the graph? By how much? Use the function to find the percentage of first-year college men expressing antifeminist views in 2004. | % of first-year college men expressed antifeminist views. (Round to the nearest tenth as needed.) % Agreeing w/ Statement
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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