EA 13,000 - P (5, 12,357) (7, 12,421) 12,500 - 12,000 - (4, 11,946), Q (6, 12,237) 11,500 - B (3, 11,302) 11,000- 10,500- (2, 10,625) 10,000 - A (1, 9954) 9500 9000 + 3 6 2.
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.
Elevation vs. Distance The following graph, obtained from GPS data, shows the elevation of a hiker as a function of the distance d from the starting point of the trail.
a. Find the slope of the secant line that passes through points A and B. Interpret your answer as an average rate of change over the interval 1 … d … 3.
b. Repeat the procedure outlined in part (a) for the secant line that passes through points P and Q.
c. Notice that the elevation function is nearly constant over the segment of the trail from mile d = 4.5 to mile d = 5. Give a plausible explanation for the horizontal line segment.
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