7 Consider f(x) =x³- 6x2+ 9x +3 defined on the closed interval . At which value of x does the absolute maximum of f on 7. the closed interval 3 occur? 1 (A) B) 1 с) з 7 2

Q: 5. Determine the minimum value of f(x) 3x on the interval [-1,1] %3D

A: Let's find.

Q: 6. Determine, with reasons, the absolute maximum and absolute minimum of f(x) = x/2 – x on the…

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Q: 2. Find the absolute maximum and absolute minimum value of f(x) = 6x – x on [1, 7].

A: Given function fx=6x-x2 To find the absolute maximum and minimum first find critical values.…

Q: Compare the graphs of y = Vx, y = Vx, y = x, y = x², and y x³ on the interval 0 0 and p and q are…

A: step:- 1 Generalization using nature of graph In interval (0,1) First draw graphs of x13,x12,x,x2,x3…

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: 5. Let f(x) = x-3x73. Use calculus to determine the critical numbers for the function.

A: Consider the  provided function, fx=x-3x23 Find the critical point of the critical point. Find the…

Q: What is the local maximum value of the f(x) = x3 - 3x +2 on [0.5, 4]

A: We are given the function  f(x) = x3 - 3x +2 on [0.5, 4]. Here, we need to find the local maximum…

Q: 2. On the interval [0,2], determine the absolute maximum, M, and absolute minimum, m. fx) 4x

A: Given fx=4x1+x2 on 0,2

Q: Find a polvnomial f(x) of degree 4 with real coefficients and the following zeros. 3,-4, 2+i 1) - 0…

A: Given,  The zeroes of the 4 degree Polynomial f(x) is 3, -4 , 2+i and 2-i.

Q: Prove that the function f(x)  =x101  + x51  +x  +1 hasneither a local maximum nor a local minimum.

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

A: Obtain the derivative of the function as follows.

Q: 3. Find the absolute maximum and absolute minimum of f(x) = 2x³ - 6x +1 on [0,3].

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Q: What is the absolute maximum value of f(z) = z³ – 3z² +4 on the interval (-1, 1]? %3D (A) 4 -2 (C) 0…

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Q: Consider the function f(x) = 2x - 9x? - 24x + 9 on the interval [-2, 5]. What is the absolute…

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Q: 10. ( ) Find the absolute extrema of the funcion f(x) = 3 Vx2 - x on the interval -1, 1.

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Q: Consider the graph of the function f(z) = 2x + 24x – 120z + 9 on the interval – 11 < ¤ < 3. - 1728-…

A: topic - absolute maximum and absolute minimum minimum = -119 mmaximum =1609

Q: 29. Determine the absolute maximum value of f on the interval [-1/2,4]. f (x) = x3 – 3x2 16 7 O -4

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Q: Consider the function f(z) = 2x+ 18z2-330z +37 defined on the interval -1, 10). Then the absolute…

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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: 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: (b) : Verify that the Intermediate Value Theorem applies to the indicated interval and find the…

A: Given , f(x)= x²-x in the interval [1,5]

Q: 7) Find the absolute maximum of the function f on (0,0) f(x) =10xe2* %3D

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Q: 1) Determine whether the function has any absolute values on [a, b].  2) Explain the results in…

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Q: Consider the function f(x) = z over the interval (-2, 2). Does the extreme value theorem guarantee…

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Q: Consider the function f(x) = x + ax + 16x2 + bx + 15, where a and b are unspecified constants.…

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Q: 11. Find the absolute minimum and maximum of f(x) = r3 - 4x2 - 3x + 3 on the interval [0, 4].…

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

A: THE EXPLANATION HAS BEEN GIVEN IN THE ATTACHED FILE.

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: Consider the function f(x) = 2x3 - 3x2-12x+c, where c is some ne location of the absolute maximum…

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Q: 9. Given f'(2) does not exist and f"(2) > 0, is x = 2 a maximum, minimum, or neither of f? Explain.

A: Given: x=2f'(2) = does not existf"2&gt;0

Q: 8. Determine the natural domain of the function Vx–1 f (x)= x²-3x+2 in interval notation.

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Q: (7) Does the extreme value theorem tell us that f (x) = ! has an absolute maximum and absolt minimum…

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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 absolute maximum and minimum values of f(x) = x3 – 12x – 5 on %3D the interval [-4,…

A: We need to find absolute max and min values.

Q: 2. Suppose that f (a, b) is an absolute maximum of the function f(x, y). Must f (a, b) also be a…

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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  f(x)= x+2sinx             in the interval [0, 2π] a) Determine algebraically all critical…

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Q: 1. Let f(x) = 4x − 4x 2 . Verify that f(x) satisfies the conditions of Rolle’s Theorem on the…

A: Note:- According to the company policy we can attempt ?️ only one question so please upload the next…

Q: 10. Use the closed interval method to find the absolute maximum and absolute minimum values of f(x)…

A: Maximum minimum value problem....

Q: Consider f(x)=x³-6x²+9x+3 defined on the closed interval At which value of x does the absolute…

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Q: 11. Find the absolute minimum and maximum of f(x) = x³ – 4x2 – 3x + 3 on the interval [0, 4].…

A: Given: fx=x3-4x2-3x+3; x∈0,4 for finding absolute minimum and maximum of given function, we draw…

Q: what is the absolute maximum/minimum of: f(x)=xln(x/4) on [0.2,4]

A: Given, function is

Q: 13. Use the Intermediate Value Theorem to show that f(x) = 2x° – 3 has a zero in the interval [1,2].…

A: Given:-f(x)=2x3-3 using the intermediate value theoremf(x) is continuous in the interval 1,…

Q: the absolute minimum of f(x) = −x3 − 14x2 − 60x − 75 on interval [−7, −5]?

A: To find: The absolute minimum of fx=-x3-14x2-60x-75 in interval -7,-5. Calculation: The derivative…

Q: (4,28) is a maximum or a minimum point of the function g(x) = -x3 + 6x? – 4. Verify whether the…

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Q: By the extreme value theorem, f(x) = x/4 – x² has extreme values on [0, 3/2]. What are the minimum…

A: Maxima and minima:…

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: 3 The absolute minimum value of f(x)=x³ on the closed interval [-1,8] is a) 0 b) -1 c) 1 2 d) -…

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Q: 4. Determine the number of zeros of the function f(2) = 2zª – 2iz³ + z² + 2iz – 1 - in the upper…

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