3 Use Calculus to find the absolute and local extreme values of f(x) = r + r on the interval [-8, 8].

Q: (c) For what values of a and b does the function (ах- 3, x< 4 f(x) = } (-x? + 10x - b, x24 satisfies…

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Q: Verify that the Mean Value Theorem applies to the function f(x) = √25-x2 on the interval [-3, 4] and…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x3 - 6x² –…

A:

Q: 3) Verify Rolle's Theorem for the function f(x) = 4x² + 6 defined over the interval [-5, 5]. Justify…

A: Rolle’s Theorem has 4 conditions to be proved.

Q: (b) Verify Mean Value Theorem for f(x)= 3x2-6x -5 over the interval[-1,4].

A:

Q: Verify that the Intermediate Value theorem

A: Concept: Intermediate value theorem is precise mathematical statement having the properties of…

Q: 19. The interval for function |(3 )/2 z-1|<2 is -2/3 ,21 (- 2/3 ,2) (-2/3 ,2] - 2/3 ,2)

A:

Q: *The interval [a, b] for a function x^3 - 4 x- - ...... 9 = 0 is [2,3] O [0, 2] O [0, 1] O [1, 2] O

A: We need to find the interval for a function f(x)=x3-4x-9=0

Q: In which interval, function f(x)=x3e-x is increasing and concave up? (0, 3(sqrt3)) (3-sqrt3, 3) (3,…

A:

Q: 3)Verify Rolle's Theorem for the function f (x) = 4x² + 7 defined over the interval |-6, 6|. Justify…

A: Rolle's theorem:- If a function f is continuous on Close interval [a,b] and differentiable on open…

Q: 19. Show that f(x) = x² + 1 is not one-to-one, using values of f (not the horizontal line test).

A: To show: The function fx=x2+1 is not one to one. Concept used: The function is one to one is and…

Q: Verify Mean value theorem for the function f(x) = 4x³ + x + 3 over the interval [0, 1].

A: Given: f(x)=4x3+x+3, 0, 1

Q: (b) Verify Mean Value Theorem for f(x)= 3x² – 7x – 4 over the interval[–1,4] .

A: Given: fx=3x2-7x-4

Q: Find and classify the extreme values of f(x)=6x^4 - 4x^6 over the interval [-2,2]

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Q: Verify Mean Value Theorem for the function f (x) = -6x+x³ over the interval [1,3]. %3D

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Q: Determine the absolute maximum and minimum values of the function f(x) =+x the interval -2sxs2. x…

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Q: Find the absolute maximum and minimum values of f (x) = x³–6x²+5 on the interval [-3,5]. %3D

A: we find the absolute minimum and maximum value at the critical points and end point on the interval

Q: 3) Verify Rolle's Theorem for the function f(x) = 4x2 + 4 defined over the interval -3, 3. Justify…

A: Solve the following

Q: Find

A:

Q: 'B4(a): Verify Mean value theorem for the function f(x) = 6x³ + x + 4 over the interval [0, 1].

A:

Q: Find all numbers C in the interval [- 2, 2] guaranteed by the Mean Value Theorem for the function…

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Q: The absolute minimum value of  f(x) = (x3/3) - ( 5x2/2) - 6x  on [-1,3] is?

A: fx=x33-5x22-6x,   -1, 3 Differentiating with respect to x, we get f'x=133x2-522x-61=x2-5x-6 Now to…

Q: (c) For what values of a and b does the function ах 3, x < 4 f(x) = (-x² + 10x – b, x 2 4 satisfies…

A: Answer:   a = 0 and b = 27

Q: Use second derivative test, If f() 16% + 10 then f(*) has a local maximum at the point * =-5 * =-2 O…

A:

Q: (a): Verify Mean value theorem for the function f(x) = 2x³ + + 3 over the interval [0, 1].

A: Hair we use the result of mean value theorem for the given interval and given function.

Q: Verify the mean value theorem for the function f(x) =(x²- 3x)(x+2) over the interval -3, 3]

A:

Q: (c) For what values of a and b does the function ах — 3, x < 4 f(x) = (-x² + 10x – b, x2 4 satisfies…

A:

Q: Find the constant a such that the function is continuous on the entire real line. (8x?, lax – 6, x2…

A: Given function f(x) = 8x2-x≥1ax-6, x&lt;4we find constant 'a' such that the function is continuous…

Q: (b) Verify mean value theorem for f(x)=x² - 5x+6 over the interval [1,3].

A:

Q: Find the domain of f (x) = V3-x x(x+2) Use interval notation, "ninf" for -∞, "inf" for oo, and "U"…

A: Given: fx=3-xxx+2   The domain is the set of all x values at which function is defined and real.…

Q: Please explain how to solve. Thank you

A:

Q: Does the Mean Value Theorem apply to f(x) = |x – 7| on the interval [1, 9]? Explain.

A: No

Q: 28. Determine the absolute minimum value of f on the interval [-1/2,4]. f (x) = x³ – 3x? 16 7 -4

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Q: 1 Express the domain of f(x) using interval notation. Use oo for oo and use U to combine 2 - 2 – 3x…

A: We have to find the domain of the given function.

Q: 24. Is the function continuous on the interval (-5, 5] ? 3х-1 f(x) = x-4

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Q: On which interval is f(x) = x³ – 12x + 12 decreasing? ㅇ (-8;2) ㅇ (-8, +8) | O (-2,+0) O (-2, 2) O…

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Q: 5. Use calculus to find the interval(s) on which the function f(x) = x-e increases.

A:

Q: (1) Find and classify the extreme values of f(x) =6x* -4x over the interval [-2,2].

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: 4. Verify Mean Value Theorem for the function f(x) = 2x ° - 6x2 + 2 in the interval %3D [a, b],…

A: given function :

Q: B4(a): Verify Mean value theorem for the function f(x) = 5x³ + x + 5 over the interval [0, 1].

A:

Q: 1- f(x) = x³. ammmed

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

Q: Use second derivative test, If f(x) = 36x + 4 then f(x) has a local 3 maximum at the point O x = -7…

A: Here we need to find the local maxima of the function.  The solution is following .

Q: Verify the mean value theorem for the function f(x) = (x² – 3x)(x+2) [-3, 3] over the interval

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Q: Let f (x)- - 6x² + 9x – 8. The absolute maximum of f(x) on the closed interval [0,5] is (1,4) This…

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Q: Find fqix(q|x) for x € {0,1} and all q.

A: Given Information: Q be the continuous random variable with pdf, fQ (q) =6q(1-q)       ; 0≤q≤10…

Q: Find and classify the extreme values of f(x)= 6x* –4x° over the interval [-2,2].

A: Given,  f(x)=6x4-4x6

Q: Number of points where f(-|x|) is non-differentiable in its domain is (1) O (2) 1 (3) 2 (4) 3

A: Given : Number of points where f(-|x|) is non-differentiable in its domain is

Q: 3) Verify Rolle's Theorem for the function f(x) = 4x2 + 6 defined over the interval [-3, 3]. Justify…

A: