In this proklem we oill study a very basic trapie madel. Consides a stretch of highway in, which travelling at an avarge Speed Y. he of Car on Cars are trappiz density u it the total amount Our Stretch of road divided by tr length. These two guantifier ave related: the less Caus an the • On the go other hand, If trapc becomer heavy, drivers will Yoad, the faster driyers are able to netuwally decrease"their speed. The so- Called parabolic model alfuntef that thie relationship is dictated by the queition equation 1- V Vmax ewhere Umox represents the Capercity af the road, and Vmar the speed limit on if. The amount of Cals pasting through our road is Called the todefie Fluux or by the product of the traric density. toh throughput, and ir give and The average Speed: F= UV Using the parabolte mbdel, find out the at. what arbrage speed y. the flux through road is moximized. %3D Our
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.
Step by step
Solved in 4 steps
