olve the problem and show your Solution. Answer the following: (Data manipulation,table of values,graph of the function, Interpretation) Problem: The local barangay received a budget of ₱100,000 to provide medical checkups for the children in the barangay. The amount is to be allotted equally among all the children in the barangay.Write an equation representing the relationship of the allotted amount per child (y-variable) versus the total number of children (x-variable). Data manipulation: Presentation using table of values: No. Of children, x 10 20 50 100 200 300 500 1000 Allocated Amount, y Graph of the function: Interpretation:
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.
Solve the problem and show your Solution. Answer the following:
(Data manipulation,table of values,graph of the function, Interpretation)
Problem:
The local barangay received a budget of ₱100,000 to provide medical checkups for the children in the barangay. The amount is to be allotted equally among all the children in the barangay.Write an equation representing the relationship of the allotted amount per child (y-variable) versus the total number of children (x-variable).
Data manipulation:
Presentation using table of values:
No. Of children, x | 10 | 20 | 50 | 100 | 200 | 300 | 500 | 1000 |
Allocated Amount, y |
Graph of the function:
Interpretation:
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