Let f be a continuous function on the interval (0, 3]. Use the following table to find the correct statement for the extrema of the function f(x). (DNE means "does not exist".) (2,3) -3 3 0 (0,1) 1 (1,2) f'(x) 3 f(x)0 0. DNE 2 -2 Absolute maximum at the point x = 1, abso- lute minimum at the point r = 3, and local minimum at the point r = 0. Local maximum at the point r = 1, local mi- nimum at the point r = whether absolute extrema exist or not. 3 but one cannot say Absolute maximum at the point z = solute minimum at the point r = minimum at the point r = 2. 0, ab- 3 and local Absolute maximum at the point z = lute minimum at the point r = is no local extremum. 1, abso- 3, and there Local maximum at the point x = 0 and local minimum at the point = say whether absolute extrema exist or not. %3D 3 but one cannot
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.
![Mathematics I (CRN: 50002)
Let f be a continuous function on the interval [0, 3].
Use the following table to find the correct statement
for the extrema of the function f(x).
(DNE means "does not exist".)
0 (0,1) 1
(1,2)
2
(2,3)
3
f'(x) 3
f(x)
DNE
-3
0.
-2
Absolute maximum at the point x = 1, abso-
lute minimum at the point r = 3, and local
minimum at the point r = 0.
Local maximum at the point r = 1, local mi-
nimum at the point x = 3 but one cannot say
whether absolute extrema exist or not.
Absolute maximum at the point z = 0, ab-
solute minimum at the point r = 3 and local
minimum at the point r =2.
Absolute maximum at the point x = 1, abso-
lute minimum at the point r = 3, and there
is no local extremum.
Local maximum at the point a = 0 and local
minimum at the point æ = 3 but oe cannot
say whether absolute extrema exist or not.
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