6. Advertising revenue for newspapers in the United States for the years 1980 through 1999 is approximated by the model R(t) = -1.03 + 7.11t - 0.30t, where R is revenue in billions of dollars and t represents the year with t = 0 corresponding to the year 1980. In what year will revenue be maximum?
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.
Advertising revenue for newspapers in the United States for the years 1980 through 1999 is approximated by the model
R(t) = -1.03 + 7.11t - 0.30t2,
where R is revenue in billions of dollars and t represents the year with t = 0 corresponding to the year 1980. In what year will revenue be maximum?
![-(-40)-(-40)-4(0.5)(300)
20.5)
40+J1600-600
x 40+J1000
x=71.62,8.377
The seller will have to sell approximately 72 itemsto maximize profit and 9 items till he gets break even profit
6. Advertising revenue for newspapers in the United States for the years
1980 through 1999 is approximated by the model
R(t) = -1.03 +7.11t - 0.30t,
where R is revenue in billions of dollars and t represents the year with t = 0
corresponding to the year 1980. In vwhat year will revenue be maximum?
7. Gravity is a bit different on Mars. A rock is kicked off the surface of
Mars. It reaches a maximum height of 96.15ft after 3.85 seconds and then
lands back on the surface 7.7 seconds after it was kicked. Determine the
equation of the flight of the rock in standard form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd89dee8c-90e3-4ae2-bce0-846fa6e8c8e1%2Ff411aaea-be36-489c-9c23-ea3227f2b449%2F06qyga_processed.jpeg&w=3840&q=75)
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