(a) on the interval [-1,0.5 and (b) on the interval [0.5,3] Find the absolute extrema if they exist, as well as all values of x where they occcur, for the function f(x) 2x -3y 3 (a) Identify the absolute maximum on the interval [-1,0.5] if it exists. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice O A. The absolute maximum is which occurs at x (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.) B There is no absolute maximum.

Q: f=x^3-21/2x^2+36x+1 For what value of x does f reach a minimum? x=? What is the minimum value?

A: Given function: f= x3 -(21/2)x2+36x+1 Differentiating f w.r.t. x, f'(x)= 3x2 -21x +36

Q: what about the local minimum?

A: To find the point(s) of local minimum in the following graph.

Q: Find the absolute minimum maximum if they exist for f(x) = x+ 4/x

A:

Q: True or false: A function may have more than one absolute maximum value.

A: We have to check given statement is true or false.

Q: Give an example that: the absolute maximum is not a local minimum.

A: Consider an example of the function:  in a interval [-2,3]

Q: = 3xe 2 on the interval [-3,3]. , and the maximum value is y Find the global maximum value of f(x) =…

A:

Q: y=2(x^3-3x+3)    Identify the absolute maximum value and where it occurs. Identify the absolute…

A:

Q: How do I find the local Maximum of this graph?    All values that have g as a local maximum? Would…

A:

Q: Where do the absolute minimum and absolute maximum occur?

A:

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.