In recent years many states have passed mandatory seat belt laws. The total number N of states that had a seat belt law in effect : years after 1984 is given by the graph below. Express the number of states with seat 20 belt laws in effect in 1987 using function notation. Then use the graph to estimate its value. Make sure to include appropriate units. ryeare b) n what year were there seat belt laws in effect in 40 states? c) When was the graph concave up? Explain how the number of states with seat belt laws was changing during this period (i.e. increase, decrease at what kind of rate). d) When was the graph concave down? Explain how the number of states with seat belt laws was changing during this period (i.e. increase, decrease at what kind of rate). Does the function represented by this graph have a limiting value? If so, estimate the value. Explain your answer in terms of the scenario. sasN
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.
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