Use the following graph of the function f(x) with domain [0,7] to find the specified information. (a)x-values for all relative minimum of f(x) (b)x-values for all relative maximum of f(x) (c) the y-value for the global minimum of f(x) (or explain why there isn’t one) (d) the y-value for all absolute maximum of f(x) (or explain why there isn’t one)

Q: Identify the labeled x-coordinate on the graph at the right as the location of an absolute minimum,…

A: Given:

Q: Identify the absolute minimum of f(x)=2x2 +x+1 over [−2,3].

A: The given function is f(x) =2x^2+x+1 over the [-2,3].

Q: Determine the critical numbers of the given function and classify each critical point as a relative…

A: Given that gx=4-2x+9x2Solution :if we have to find critical point then first derivative equal to…

Q: Use a graphing calculator to estimate the local maximum value of the function and local minimum…

A: To find the maximum and minimum value by using graph of the function

Q: Indicate the values of the global maximum and global minimum for the function, f(x) = xlnx, as well…

A: f(x)=xln(x)f'(x)=ln(x)+x.1xf'(x)=1+ln(x)now f'(x)=01+ln(x)=0ln(x)=-1x=e-1x=0.3678

Q: Given the function yx-4x. Determine 1. intervais of increasing and decreasing points of local…

A:

Q: 1. Use the first derivative test to find the local minimum and maximum points of the graph of f(x) =…

A:

Q: Sketch the graph of a function that has an absolute maximum, alocal minimum, but no absolute minimum…

A: Consider the provided information, Sketch the graph of a function that has an absolute maximum,…

Q: Estimate and classify the critical points for the graph of the function. 4. -4 2

A: A critical point of a function of a single real variable, f(x), is a value x0 in the domain of f…

Q: Find the minimum of f(x) = 3 + 6*x + 5*x2 +3*x3 + 4*x4 in the range of [-2, 1]

A: the given function is f(x)=3+6x+5x2+3x3+4x4 find the derivative  f'(x)=6+10x+9x2+16x3 find the…

Q: Find the absolute minimum value for on the interval [-1,1]

A: In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol…

Q: What is the global minimum of the function f (x) = x/2 (x – 4)?

A: Find the critical points and evaluate the given function at critical point.

Q: SKetch the graph off over the indicaed Inteval and locate all absolut and relative maxımum and…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Use a graphing calculator to estimate the local maximum and local minimum values of the function to…

A: Local extrema.

Q: Find the absolute maximum and minimum values of ƒ(x) = x2 on[-2, 1].

A: Given,  fx=x2 on −2,1

Q: Does x=6 belong to a local maximum or a local minimum? Does x=0 belong to a local maximum or a local…

A: Here we have,  differentiate with respect to x

Q: Sketch the graph of a function on the interval [3,9] that has an absolute maximum at x=5 and an…

A: Ques:-   Sketch the graph of a function on the            intervel 3,9 that has as absolute…

Q: Use a graphing utility to approximate (rounded to two decimalplaces) the local maximum value and…

A: Given: fx=x3-2x2-4x+5; -3<x<3 For finding values of local maxima and local minima, we draw…

Q: Draw the graph of f (x) = 3x +7/5x - 25 in the window [0, 25] by [0, 50]. Use the trace feature of…

A: Given: fx=3x+75x-25 in the window [0, 25] by [0, 50].

Q: Use technology to find a local maximum and2 local minima of the graph of the functiony = x4 - 4x3 +…

A:

Q: Find the absolute minimum value of f(x) = + 2 In x + 5 for - < x < 5.

A:

Q: Sketch the graph of a function that has neither a local maximumnor a local minimum at a point where…

A: Sketch the graph of a function that has neither a local maximumnor a local minimum at a point where…

Q: consider the function f(x) = -x/(8x^2 +1), where 0 ≤ x ≤ 2 What’s the absolute maximum value equal…

A: Given data: The given function is f(x)=-x/(8x^2 +1). The given limits of x are [0, 2]. The…

Q: Identify the absolute minimum of g(x)=−2x2 −x+1 over [−2,4].

A: Absolute minimum:The absolute minimum of a function f on the interval [a, b] will occur either at…

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A:

Q: If f is a continuous, odd function and f(c) is a relative maximum, then f(-c) is a relative minimum.…

A:

Q: Find the locations of local minimum and maximum of X⁹ x⁹-4x8 using the second derivative test. 32…

A: let f(x)=x9-4x8Differentiate with respect to x 9x8-32x7=0x7(9x-32)=0⇒x=0,x=329  are the critical…

Q: Find the absolute extremum within the specified domain. 21) Minimum of f(x)=(x2+4)2/3; [-2,2]

A: According to our policies we are allowed to solve one question at a time. Kindly repost other…

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A:

Q: show that the function has neither an absolute minimumnor an absolute maximum on its natural domain.…

A:

Q: If f(x) is a continuous, odd function and f(c) is a relative maximum , then f(-c) is a relative…

A:

Q: Find the relative maximum / minimum values of the function x- 2 f(x) = x+2 State where the function…

A: Given that, the function is fx=x-2x+2. Differentiate the function fx=x-2x+2 with respect to x as…

Q: What is the absolute minimum value of the function f(x) = x - 3x2 on the interval [-2, 4] ?

A: Given function is f(x) = x3 - 3x2 ; -2 ≤ x ≤ 4 We have to find its minimum value.

Q: 1) Explain the differences between an absolute minimum and a local minimum.

A: An absolute minimum occurs at the x value where the function is the smallest, while a local minimum…

Q: Find the absolute minimum value of f(x) = 9x² - 5 x + 14 on the interval [0, ∞). Note: You need to…

A:

Q: 6. Determine the x-value of the absolute minimum of f(x) = -2x4 + 4x³ - 1 on the closed interval…

A: Given:       fx=-2x4+4x3-1     f'x=ddx-2x4+4x3-1    f'x=-8x3+12x2

Q: -, Determine the location and values of the absolute maximum and absolute minimum for the given…

A:

Q: 4. Find the absolute minimum and absolute maximum values of on the interval 1,2

A: The function is given by,

Q: ¥ 5) Find all the critical points of f(x)= = = 2 and determine if they are a relative maximum,…

A:

Q: Find the global minimum of the function f(x)=2x^3+3x^2–12x+4 on the interval [-4,2].

A:

Q: f(x) = }x* – }x³ – x² + 2x – 1 - -

A: We have the given function as fx=14x4-23x3-12x2+2x-1             ⋯⋯1 In order to find…

Q: Find all the critical points of  f(x) = 3x4 - 40x3 + 150x2 and classify each as a relative minimum,…

A: Find f'(x) using exponent rule.

Q: Sketch the graph of a function on [-1, 2] that has an absolute maximum but no absolute minimum.

A: (a) The 4th graph is the correct graph. In the interval [-1, 2] the maximum value for the function…

Q: Can you help me step by step?

A: Since, the function f is an even function, so by definition of even function:

Q: intervals

A: A function is increasing if when y is increasing with respect to x ot vice versa. Hence, Given…

Q: Find the absolute minimum value on​ [0,∞​) for f(x) = 2x2 -12x + 6

A: To find the absolute minimum value of the function on the given interval.

Q: 4, Find all critical points and itentify them as local maximum points local minimum points, or…

A: The given function f(x)=x2-121

Q: What is the x-coordinate of the global minimum of the function f(x) = x – 3 ln x – 2 for the…

A:

Q: a)f(x) = 3(x² – 1)° in the intervals (-1,2)

A: I have solved using derivative test

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.