The wholesale price in dollars of one pound of ground beef is modeled by the function f (t) = 3.08 + .57t - .1t2 + .01t3, where t is measured in years from January 1, 2010. (a) Estimate the price in 2011 and find the rate in dollars per year at which the price was rising in 2011. (b) What is the percentage rate of increase of the price of one pound of beef in 2011? (c) Answer parts (a) and (b) for the year 2016.

Q: The number of citizens (N) of barangay Alapan, Imus Cavite in t years is predicted to increase and…

A: N(3)=7 (3)^4-4(3)^3+150(3)+17500

Q: The amount of fish exported each year can be approximated by A(t) =15(0.96)t  million pounds, where…

A:

Q: According to the Association of American Railroads, Class I freight railroads are the line-haul…

A: The average rate of change per year in F from 2005 to 2007 is $4.2 billion/year.

Q: Assume S=0.6Y+19 describes the projected relationship between  S⁢ , sales of a company (in millions…

A: Given that the model S=0.6Y+19 describes the projected relationship between S , sales of a company…

Q: The national health care expenditure H (in billions of dollars) can be modeled (that is, accurately…

A:

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.