While traveling across the country on a road trip, Hadassah passes the Indiana state line. Let d be the distance in miles of her car from the Indiana state line, and let į be the number of minutes since she passed the Indiana state line. The distance d is a function of the time t and is represented by the function f, defined by d= f(t)= 0.0181² +1.07t What is the meaning of f(14)– f(9)? The time elapsed as she car moved from 9 miles to 14 miles past the state line. The change of distance of your car in the first 5 minutes after she passed the state line. The average speed of her car from t = 9 to t= 14 minutes. The average speed of her car as it moved from 9 miles to 14 miles past the state line. The distance traveled in the time interval 9 to 14 minutes since she passed the state line.
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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