Suppose the value of Tech Advanced stock (in dollars) is given by g(t) where t represents the number of days after January 1, 2014. Express the values of the following stocks in terms of the function g. The value of TechPrime's stock, h(t), is always half as large as the value of TechAdvanced`s stock. The value of NewTech's stock, n(t), is always 10 dollars more than the value of TechAdvanced's stock. The value of VirtualTech's stock, p(t), is always the same as the value of TechAdvanced's stock two weeks later.
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.
Suppose the value of Tech Advanced stock (in dollars) is given by g(t) where t represents the number of days after January 1, 2014. Express the values of the following stocks in terms of the function g.
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The value of TechPrime's stock, h(t), is always half as large as the value of TechAdvanced`s stock.
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The value of NewTech's stock, n(t), is always 10 dollars more than the value of TechAdvanced's stock.
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The value of VirtualTech's stock, p(t), is always the same as the value of TechAdvanced's stock two weeks later.
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An investment company, Fortune10, sells TechAdvanced stock to the public but charges twice as much as the price of the TechAdvanced stock and also assigns a 5 dollar fee. Let the function kk model the price of buying TechAdvanced stock in terms of the number of days since January 1, 2014.
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