Let f(x) = x³ –x² – 12x+2. Find the global maximum and minimum of f(x) over the interval [-2,1]. (Explain basic steps.)

Q: Find the absolute maximum value of f(x) = x² – 2x + 8 over the interval [0,5|

A: The objective of the question is determine the absolute maximum value of the given function.

Q: Find the linearization L(x) of the function at a. 9 f(x) = a = 3 - L(x) =

A: We have to find the linearization L(x) of the function at a.  We have, f(x)=9x and a = 3

Q: Find a cubic function f(x)  = ax3 + bx2 +cx +d thathas a local maximum value of 3 at x =-2 and a…

A: At x=-2 , y=3  So,  at x=1, y=0

Q: The function f(x) = xvx – x² defined on the closed domain [0, 0.9] has an absolute minimum value of…

A:

Q: 4) Let f(x) = x* – 2x -1 be defined on the interval [-1,3]. Find the maximums and the minimums.

A: The given function is defined  f(x) = x4 - 2x2 - 1 Over [-1,3] To find minimum and maximum value of…

Q: Find the global maximum of f(x) = x(4−2x) over the interval (−∞,∞)

A: Given:The function is f(x) = x(4-2x) .The interval is (−∞, ∞).

Q: Find the critical point for f and then use the second derivative test to decide whether the critical…

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Q: 3:- Find the maximum value of the function f(x, y) = x²y on the line x + y = 3.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the global maximum and global minimum of f(x)=x22x in the interval [−1,3].

A: We first find the critical points by solving f'(x)=0

Q: Determine the absolute maximum and minimum values of f(x) = x²e on x = [-5, 1].

A: Given: fx=x2ex on x∈-5, 1 To find the absolute maximum and absolute minimum of the given function on…

Q: f(x) = x2 -x-7 is The relative maximum value of and its relative minimum value is

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Q: Find the minimum value of f (x) = 7x² – 2x + 4 on the interval (0, 1].

A:

Q: Find the absolute maximum/minimum of function f(x) = x3 - 16x + 1 %3D

A: fx=23x3-16x+1 to find the critical points take derivative=0 ddx23x3-16x+1=0 ddx2x33-ddx16x+ddx1=0…

Q: The absolute minimum of f() = x² +3x – 1is

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Q: (b) Find the global maximum and minimum values and indicate where they occur. f (x) ,x, ) = 2x, + x,…

A: Find the global maximum and minimum values and indicate where they…

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: Let f(x) = x³ - 3x². Find the absolute minimum value of f(x) on the interval [1, 4].

A: The given function,  f(x)=x3-3x2 on the interval 1,4

Q: Find the maximum value attained by the function x² + xy + y² on the set {(x, y) : x² + y² < 2}.

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Q: Find the absolute maximum and minimum values of ƒ(x) = ex - 2x on [0, 1] .

A: Consider the given function.

Q: (B) The function f(x) = x² + x +1 has no fixed point, prove that.

A: Let X be a nonempty set and f : X → X. A point x ∈ X is a fixed point of  f, if f(x) =x.  If no…

Q: 2 The function defined by f(x)= x-3x for all real numbers x has a relative maximum at x = %3D

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Q: Find the global minimum of the function f (x) = 2x’ + 3x² – 12x + 4 on the interval [-4,2].

A:

Q: Find the global maximum and global minimum of f(x)=x√x in the interval [2,3].

A:

Q: How do I solve this?

A: Global maxima or minima of f(x) in [a, b] is basically the greatest or least value of f(x) in [a,…

Q: Give an example that: the f'(c) 0 but c is not a local maximum or local minimum.

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Q: ) Because f(-1) and f' changes from negative to positive at x = f(-1) = -7e-1 is a local (and…

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Q: Find the absolute maximum and absolute minimum f(x) = + x2 24x over the interval 2, 6|. -

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Q: Let f(x) be maximum and g(x) be minimum of {x|×|, x² | × [} then

A: 9

Q: Let f(x) be maximum and g(x) be minimum of {x|×|, x² |x} then

A:

Q: Find the absolute maximum/minimum value for f(x)=x² – 4x+1 on the interval [(-3, 3] 9.

A: Given: fx=x2-4x+1 and x∈-3,3   The Power law: ddxxn=nxn-1

Q: Find the global maximum and global minimum of f(x)=2x in the interval [−1,3].

A: Given function is Differentiating with respect to x, we get Now, f'(x) =0 for no value of x and…

Q: Let f(x)=x^2 -x^3.  Find the global maximum and the global minimum value of this function on the…

A: Given: fx=x2-x3 for finding global maximum and global minimum, we finding increasing and decreasing…

Q: Let f (z) = =- 2a? – 4z +1. On the interval -1,3, the absolute maximum value of f is and the…

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Q: Determine the global maximum and minimum function a)f (x): x² + 1 in the intervals [0,2]

A:

Q: Let f(x) = x² – a³. Find the global maximum and the global minimum value of this function on the…

A: Given data:   The expression for the function is f(x)=x2-x3. The given limit of the function is [a,…

Q: Determine f such that f′′(x) = 12x − 1 and 1 is both a critical number and a y- intercept of f

A: Given:  and 1 is both critical number and y-intercept.

Q: The absolute minimum of f(x) =x² – 4x On [0,3] is y= %3D 540 .BO -4 .CO -3

A: We use first derivative test to find absolute minimum.

Q: Find the absolute maximum value of p(x) = -x² – x + 1 over er[-1,1].

A:

Q: Find the value of x at which the absolute minimum occurs (if it exists) for the function f(x) = -x2…

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Q: Let f(x) = +2x2 - 2. Find the global maximum and minimum of f(x) over the interval [-1,1]. (Explain…

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

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Q: Find a cubic function f(x) = ax3 + bx2 + cx + d that has a local maximum value of 4 at x = −4 and a…

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Q: Find the absolute maximum and minimum of the function f(x) = x3 - x2 +x %3D on interval [0,3]

A: Given function is f(x)=x^3 -x^2+x on the interval [0,3] first lets find critical points find…

Q: Find the global maximum and global minimum of the function f(x)=x2−16x on the interval [−4,−1].

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Q: Determine the global maximum and minimum function a)f(x) = 3x2 – 12x in the intervals [0,3]

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Q: What are the absolute maximums and minimums of z(x) over its domain?

A: Given To find what are the absolute maximums and minimums of z(x) over its domain.

Q: Find the global maximum and minimum of the function f(x)=√3−2x on the interval [−3,1).

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

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

A: I have solved using derivative test

Q: Find the absolute maximum and the absolute minimum of f(x) = x^3 − 3x^2 on the interval [−1, 3].

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.