Show that the interval [0,1) does not have a maximum element; that is, there is no largest number less than one.

Q: 2- find the absolute max.and min. of the on the closed triangle function P : x* + y Plate bounded by…

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Q: Find the number in the interval [−1, 1] such that the sum of the number and its square is a maximum.

A: Given: The given interval is -1,1. We have to find where the sum of the number and its square is a…

Q: Use a computer algebra system to find the maximum value of |f"(x) on the closed interval. 3 1 3 2…

A: Given:

Q: The absolute minimum value of the function f(x) = 4x2 – 8x + 8 over the interval [0, 5] O 4 O 5 O 6…

A: To find absolute max/min we have to find local max/min in a given interval and also function value…

Q: The absolute minimum value of the function f(x) = 7x2 - 14z +9 over the interval [0, 8] O 10 O 2 O…

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Q: What is the global maximum of the function, x2 f(æ): 3 on the interval[-2, 2] ? 3 2

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Q: Find the maximum value of x2+20 divied by x+1 on the horizontal span of 0 to 10.

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Q: The pair of numbers whose sum is 22 and whose product is as large as possible is (Use a comma to…

A: Let, x be one of the number from the pair who's sum is 22 and whose product is as large as possible.…

Q: If  f has a local minimum value at , show that the function g(x)  =-f(x)has a local maximum value at…

A: Let  g(x)=-f(x) g'(x)=-f'(x) If f(x) is increasing in interval (a,b) , then  That is if f(x) is…

Q: 2. Of all numbers whose sum is 30, find the two that have the maximum product. That is, maximize Q =…

A: To Determine: of all numbers whose sum is 50 ,find the two that have the maximum product .That is…

Q: Consider the problem of finding the local minimum points of the function f(ï) = -4 +" over the…

A: Given

Q: Find the absolute minimum and absolute maximum values of fon the given interval. Rx) = x- In(7x), 2…

A: The given function is fx=x-ln7x,  12,2.

Q: The pair of numbers whose sum is 10 and whose product is as large as possible is. (Use a comma to…

A: The objective of the question is determine the possible values for maximum product and the product…

Q: Let f(x) be the perimeter of a rectangle with an area 36units? and one side with length x. f(æ) =…

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

A: Given Data The function is y=1-eˣ/ eˣ+1.   Differentiate the function y=1-eˣ/ eˣ+1 with respect to x…

Q: Use Picard's theorem, find the largest interval for which the IVP (x – 8)(x – 1) -y'%3D (x-6)(* +1)…

A: To find the largest interval on which existence and uniqueness guarantees a unique solution. For…

Q: Given ƒ(x) = ax2 + 2bx + c with a >0. By considering the minimum, prove that ƒ(x)>= 0 for all…

A: Consider the given function f(x) = ax2+2bx+c with a > 0It is required to prove that:

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

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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: Identify the absolute minimum of p(x)=−x2 −1 over [−1,5].

A: Find the absolute minimum of the function on given interval.First find the derivative of the given…

Q: an I ask how the maximum and mininmum points were obtained?

A: We need to find max and min points.

Q: What is the absolute minimum value of p(x)=2x2-x-2 over [−2,6]?

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Q: Let A be a positive real number. If the absolute minimum value of f(x) = Ax³ – 40x³ on 0, 00) occurs…

A: fx=Ax5-40x3 Differentiating with respect to x, we get f'x=A·5x4-40·3x2=5Ax4-120x2 Now to find…

Q: Let A be a positive real number. If the absolute minimum value of f(x) = Ax³ – 90x³ on [0, 00)…

A: we  are given f(x)=Ax5-90x3 and absolute minimum at x=cAk we have to find c?

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

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Q: Find the absolute maximum of h(x)=x^2−x−2 over [−3,6].

A: Given query is to find the absolute maximum for function h(x) ove the interval  [−3,6].

Q: Find the giobal maximum/ minimum points of a. flx) = [-s, -4] X-1 on 3+X

A: Topic- Application of Derivative

Q: 1. Of all numbers whose sum is 70, find the two that have the maximum product. That is, maximize Q =…

A: Let such two numbers whose sum is 70 and have the maximum product are x and y. So, we have x+y=70…

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

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Q: By choosing x, find a maximum of xre-x, if r>2, otherwise the function goes to infinity at x=0.

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Q: Find the absolute maximum of p(x)=x2 −x+2 over [0,3].

A: We have to find absolute maximum of f(x) in given interval .F(x) is given as:

Q: Prove that if A has n as a minimum then B = {x ∈ R | ∃a ∈ A, x = −3a} has −3n as a maximum

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Q: 4. Prove that the interval (0, 1) does not contain a smallest value x.

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Q: Let x and y be two positive numbers such that x+2%3D50 and (x+1)(y+2) is a maximum. Find the value…

A: topic - application of derivatives

Q: Let a, B be positive numbers. Find the absolute maximum value of f(x) = x°(1 – x)*, 0 < x < 1.

A: To find the absolute maximum of the given function.

Q: Use the first- and second-order optimality conditions to find all local minimums of f : x € R² → ¤1…

A: The given problem can be expressed asMinimize f : x1+3x2Subjected to h : x12-5x22+5 Firstly, we will…

Q: Use the algorithm for finding extreme values to determine the ABSOLUTE MAXIMU OLUTE MINIMUM values…

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Q: It is possible for the absolute maximum of a function on a closed interval to occur at:

A: An absolute maximum must occur at a critical point or an endpoint, and x = 0 is the only such…

Q: Use the Cauchy-Schwarz inequality to solve the following max/min problem: If the (long) diagonal of…

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Q: Find the following: (a) two nonnegative numbers whose sum is 12 such that their product is an…

A: For part (a), The sum of two number is 12. The product of two number is absolute maximum. For part…

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

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Q: ) Find all critical points of f(Xiy> and dlassify each as a celative maaimum, celatine minimum, or a…

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Q: Suppose the product of x and y is 49 and both x and y are positive. What is the minimum possible sum…

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Q: 2: Find the minimum value of f on the closed interval [-3,8]. Justify yokr answer..

A: To find the minimum value of f on the closed interval -3,8

Q: Consider two nonnegative numbers x and y such that x+y=10. Maximize and minimize

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