Life Span On the basis of data and projections for theyears 1910 through 2020 the expected life span ofpeople in the United States can be described by thefunction f (x) = 11.027 + 14.304 ln x years, wherex is the number of years from 1900 to the person’sbirth year.a. What does this model estimate the life span to befor people born in 1925? In 2007? (Give eachanswer to the nearest year.)b. Explain why these numbers are so different.
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.
Life Span On the basis of data and projections for the
years 1910 through 2020 the expected life span of
people in the United States can be described by the
function f (x) = 11.027 + 14.304 ln x years, where
x is the number of years from 1900 to the person’s
birth year.
a. What does this model estimate the life span to be
for people born in 1925? In 2007? (Give each
answer to the nearest year.)
b. Explain why these numbers are so different.
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