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.
1. Use function notation to represent that the distance on the road (in miles) that corresponds with 3 inches on the map is 84.
2. Define a function h to determine the Hare's distance from the starting line in terms of the number of seconds, t, since the start of the race.
3. Solve j(t)=0 for t, then describe what your solution represents.
4. The distance between the tortoise and hare 13 seconds after the beginning of the race.
5. The distance of the tortoise from the finishing line 20.7 seconds after the start of the race.
6. An additional 20 meters to the Hare's distance from the starting line
7. Use function notation to represent that the distance on the road (in miles) that corresponds with 3 inches on the map is 84.
8. Recall that a function's domain describes the possible values that the independent variable of a function can assume/take on.
What is the domain of the function that defines the actual distance (in miles), d, in terms of n, the number of inches measured on the map. Use interval notation.
9. Recall that a function's range describes the possible values that the dependent variable of a function can assume/take on.
What is the range of the function that defines the actual distance (in miles), d, in terms of n, the number of inches measured on the map. Use interval notation.
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