On which interval is f(x) = x – 12x + 12 decreasing? o (-2, 2) o (-00, 2) o (-0, -2) U (2, +0) ㅇ (-8, +8) ㅇ (-2,+0)

Q: Find all critical points for the function f(x) V(x2 - 4). %3D

A: Given function f(x)=x2-4  To Find all critical points of the given function.

Q: The function f(x) =3 x4-4 x3-12 x2+1, is increasing on the interval

A: f(x) = 3x4-4x3-12x2+1f'(x) = 12x3-12x2-24xf'(x) = 12x(x2-x-2)f'(x) = 12x(x2-2x+x-2)f'(x) =…

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 the absolute maximum and minimum of f (x)=x* – 2x -x - 4x +3 on the closed interval [0, 4]. а.…

A: fx=x4-2x3-x2-4x+3 Differentiating wrt x, we get  f'x=4x3-6x2-2x-4 Putting f'x=0, we get…

Q: Find and classify all critical points of the function f(r, y) = 12x² +y° - 12ry.

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Q: Verify Rolle's theorem for f(x) = x* – 4x+8 over the interval [0, 2].

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Q: Find all relative extrema in the function k(x) = (x2 – 4)-2 on the interval [-3, 3].

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Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: Find the maximum and minimum value of the function f(x) = xe¯¤ on the interval (0, 2]. %3D

A: If you like the solution then please give it a thumbs up.. The Answer is:        Maximum value = 1…

Q: Find the critical numbers of the function: f(x) = x3 - 3x2 +1 %3D | Select one: а. X-0, х32 b. x=…

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Q: Find the absolute extrema of the function on the closed interval.                   f(x) = x3 + 6x2…

A: To find the absolute extrema of the function on the closed interval. first differentiate and find…

Q: Find the absolute extrema of the function on the closed interval.                          f(x) =…

A: The given function is Solve the absolute extrema on closed interval [0,4] by finding its derivative…

Q: Find the absolute extrema of the function on the closed interval.                          h(x) = 5…

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Q: The function f(x) = −2x³ + 3x² + 36x has two critical points, c₁ and c₂. Find them and use the…

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Q: 1. f(x) = x² +x – 1 for all values of x -

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Q: Suppose that f'(x) = (x − 1)³x² x + 3 Determine the interval(s) on which y = f(x) is decreasing.

A: To find out the intervals on which the function is decreasing.

Q: Find linearization L(x) of f (x) = Vx at a =4 and use to approximate 7.8.

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Q: -2 Find the interval(s) where f(x) =- 64-x2 is continuous.

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Q: Find the absolute extrema of f(x) = x³ - 6x - 1 on the interval [-2,3].

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Q: Find and classify the stationary points of f(x) 2x} + 4x,x3 – 10x,x, + x}

A: Given,     f(x)=2x13+4x1x22-10x1x2+x22

Q: Find the absolute maximum and minimum of f(x)=x² - 3x on the interval [-1, 3]. Express your answer…

A: The points of local maximum and minimum can be obtained by differentiating the function and equating…

Q: 5. Prove f(x) = e* + x has a root on the interval (-1,0) using the Intermediate Value Theorem.

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Q: If f(x) < 0 for all real numbers x then f is decreasing on (-o, 00).

A: Proceed as shown below

Q: The function f(x)=(2-x)/(3) is continuous at

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Q: Prove that f(x) = x 2 takes on the value 0.5 in the interval [0, 1].

A: We have to prove that f(x)=x2 takes on the value 0.5 in the interval [0, 1].

Q: Find the values of k that make the function continuous. Jk² + 18x, x > -3 f (x) = kx, x < -3

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Q: 8. Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6].

A: Given : The function is f(x) = 6x + 4 +24x and the closed interval [ 1, 6 ].

Q: The critical points of the function f(x) 36z2 - 2x occur at 2- 0, r +4.00 0, z +2.40 %3D I0, z -…

A: We have to find the critical points of the function f(x)=36x2-2x4.

Q: Find the absolute extrema of the function on the closed interval.

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Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: Determine the maximum number of turning points of f. 6. f(x) = (x – 2)2(x + 4)2 7. Identify the end…

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Q: Find the absolute extrema of the function on the closed interval.                            y =…

A: y = 3x2/3 − 2x,                                   [−1, 1]   absolute extrema of the function = ?…

Q: Locate the absolute extrema of the function on the closed interval. f(x)= x³ 12x, [0, 4] -

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Q: How must f(0) be determined so that the function f(x) = x2-x ニー x0, is continuous x-1 at X= 0?

A: Let f be a real function . Let a be any point in its domain . If limx→afx exist and equal to fa Then…

Q: 7. Find the absolute maximum and minimum of f(x) = x!/² ( on the interval [0, 4]. %3D

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Q: The function f(x) = 3 x4-4 x3-12 x2 +1, is decreasing on the interval OA (-00,-2)U(0,2) OB…

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Q: Find the intervals on which the function f(z) = z' - 6z + 10 is increasing and decreasing. %3D

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Q: 3. Over which interval is the function f (x) = 1 + 2ex -3x increasing?

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Q: Q3. At what points are the functions continuous 1 x+3 y = X-2 Зх, y = x2-3x-10 '

A: We find the point of discontinuity of the given function

Q: The interval on which f(x) = VI-x is decreasing where x€ [-1.1] is

A: Given function f(x)=1−x2   on  [−1,1]

Q: 2 The function f(x)= (x² – 1) ³ , is decreasing on the interval (- 00,-2)U (0,2) AO (-1,0) U (1, ∞ )…

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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: Find all points c satisfying the conditions of the MVT for the function f(x)=x3−x in the interval…

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Q: Find a and b so that the function = { ax + b, 8x – 8x? + 4, ах + b, х -2 is both continuous and…

A: Continuity at x=-28-23-8-22+4=a-2+b-64-32+4=-2a+b-92=-2a+b→1

Q: Find the absolute extrema of the function on the closed interval. f(x) = x3 - 12x, [0,6]

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Q: Find and classify the critical points of the function f(x, y) = x³ – 10.5æ? – y? + 5 - -

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Q: 2. Consider the function а(т — 2) Vx +2 – 2 - if x 2, 2x 2 x² - where a, b, c are real numbers.…

A: Given function is  f(x)=a(x-2)x+2-2   if x&lt;2b                     if x=21x-2-cx2-2x  if x&gt;2…

Q: If F(X) is an antiderivative of *-2 + x-', then what is the value of F(1) - F(-1)?

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Q: Find all critical points for the function f(x) = (z² – 4) . %3D

A: To find the critical points of f(x), find the derivative of f(x) and equate it to zero.

Q: Verify Rolle's theorem for f(x) = x² - 9x +6 over the interval [0, 3].

A: