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.
Please explain in 2-3 sentences using definitions. Thanks a lot for now.
![Short Answer Questions
A Consicler the sequence
20
Find on upper baund ond
n+1nEIN
the limit af this sequence, if they exist
* Let aER GiLe on example of nested intervals of each af
positice length such that the intessection contains the unique
element a.
Consider the sequence ,1,2,1,2,3, 4,2,3,4,4,2,3,4,5,-.. (
Determine the limit superior ord Limit inferior of this sequence,
if they exist
O for n>a, let an= 50 Determine for which n, lanl<4
* Describe al continuus functions y-flx) which are defined for
all xER and satisfy the equation flxl= 1
Describe all functions y-flxl which are defined for all XEIR
ond satisfy the equation flxl=1
O Consider the sequence 1,
1.
Determine the limit superior ond Cimit inferior of this sequence
if they exist.
O Find the constont C so that the limit Lim x+x+ C exist
X43 x-5x+b
O Give on exemple of a function with two zeas(ficle0),
icn cannot be fourd by the bisection method (You may stetch oraph
one of
Determine at which points the function
is continuous
わxl=} x ×E9
if XERIO](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9968669c-02fd-4f8c-8067-f2abd5ddab2d%2F75f51764-9b80-4c4c-8aea-a35a8cf9b9c7%2Fksxt3xr_processed.jpeg&w=3840&q=75)
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