Find the open intervals on which the function is increasing or decreasing. Apply the First Derivative Test to identify all relative extrema. f (x) = 2-r(),r (x) = (r- 6)2-7 Enter the value of the absolute maximum in the box and upload your work in the next questions.

Q: y' + = 2x/y;;y(0) = 2 3. + 3x²y = 6x²; y(1) = -2 dx 4.

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Q: 2)Given :f ( x ) = 2x3-3x2-36x+14 Find the critical numbers.b)Find the relative (local) extrema.

A: Given,            fx=2x3-3x2-36x+14To find : a Find the critical numbers.                 b Find the…

Q: y(x - 6y)dx - x(2x - 9y)dy = 0; when x=1, y=1 a. y?(2y-3x) = 3x2 O b. y?(2y+3x) = x² c. y2(3y-x) =…

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Q: Write out the MacLaurin polynomial of degree 12 of the function h(x) = cos(x2). (b) Use you answer…

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Q: Suppose we have f (x, y) = x + 1' What is the level curve for f (x, y) = 5 ? (a) a parabola (b) a…

A: Let's find.

Q: V 8-x² X 2 4.

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Find the length of the curve defined by y = 3 In 3 from x = 8 to x = 9.

A: Use derivative of function and length of curve formula .

Q: The base of a three-dimensional figure is bound by the semi-circle y = V9 x. Vertical cross sections…

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Q: Find the exact length of the cur x =t sin t y =t cos t for 0 <t < 1.

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Q: How.S You Are to ConSÅruct an afen rectangular boxfro4- 12 t? of material what dimensions w resuttin…

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Q: (бх2 — 4x + 5)dx (2x – 1)(3x + 4)dx Jx(vz - 1)dx

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Q: For 4. Sketch the region enclosed by the given curves. Find its area. Make sure you show how you…

A: see below the answer and explanation

Q: V = 75(1.2)', where V is in dollars and t is the number of years since 1975. Find the rate, in…

A: The value of a particular rocking chair is well approximated by V=751.2t

Q: Just algebkaiçal fing the inverse function of f in formally VeRify that f(e10)) =x and

A: Here, to find the inverse of each function and then verify f-1(f(x))=f(f-1(x))=x

Q: For 6. the region bounded by the given curves is rotated about the specified axis. Sketch the region…

A: Given

Q: 4. Consider the integral (a) Draw the region of integration. (b) By reversing the order of…

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Q: 2 dx + ( 2x-y+3) dy = 0 ans. y + C = - In |2y-y+4|

A: See the details solution in below

Q: Let the cost function be C(x)= x2 / 8 + 4x + 200 and the unit is sold at price of p = 49 - x dollars…

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Q: dy S4ト9-とト」

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Q: Hwes You are to construct an ofen rectangulaK box from 2 t? of material what dimensionswi4 resultin…

A: g

Q: Given f''(T) 9 sin(3r) and f'(0) 6 and f(0) = 3. Find f 2.

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Q: The base of a three-dimensional figure is bound by the line y = x +2 on the interval [0, 4].…

A: Let's find.

Q: Find the domain of this 2-variable function and sketch it (shade it in): f (x, y) = V1– x² – y2 y 1…

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Q: A rectangle is expanding such that its length is always 4 times its width. If the width is…

A: Let's find.

Q: 3X-1 xp +4

A: Follow the procedure given below.

Q: 3x-4 Y = Arctan

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Q: A balloon is released from the ground 60 meters from an observer. The balloon rises directly upward…

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Q: Consider the following. x = 9 sin?(t), y = 9 cos?(t) (a) Eliminate the parameter to find a Cartesian…

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Q: w3sec?xdx – (1 – 2w²tanx)dw = 0

A: Let's find.

Q: Consider the following function. f(x) = 16 – x2/3 Find f(-64) and f(64). f(-64) = f(64) = Find all…

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Q: Find the dimensions of a rectangle with a perimeter of 140 feet that has the maximum area. The side…

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Q: Let k(x) = tan−1 x. Find the value of k(9)(0), the 9th derivative of tan−1(x) at x = 0.

A: Given

Q: What is the value of x in the diagram below? Round your answer to the nearest hundredth. Show all…

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Q: Find the exact sum of the series 1 - 1 + (1/2!) - (1/3!) + (1/4!) - (1/5!) + (1/6!) - ...

A: Topic:- sequence and series

Q: 5) The solution of the volume of triple integrals r1-x 5-r dz dy dx is:- 30 A) 5 20 В) з С) 30

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Q: Question 13 4x-7x+31x-38 (x+4)(x+2) fraction? dx is equivalent to which of the following integrals…

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Q: #4. Find the equations of the tangent lines to the relation 3y = x² - 4y when x 2.

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Q: 5.SUPPOSE tu at fex)= XJgcK)· If 903)=16 and g C3)=-5.what is f'(3)?

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Q: Si x³VI+x* dx? After substitution is performed, what is equivalent to 82 4 vũ du 82 Vũ du 82 Vu du 4…

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Q: A medical researcher believes that the human immune system produces antibodies to a particular…

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Q: Solve the ff first order DE using integration method, by substitution, or bernoulli's equation. show…

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Q: What is the value of csc(0) if the terminal side of the angle 0 intersects a circle at the point…

A: At first we want to find radius of the circle.

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

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Q: Given: -8 17 sece = -17/15 17/8 -17/8 17/15

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Q: coordinates

A: We have to choose the correct option according to the given information

Q: Learning Task 2: Expand each function (using the appropriate technique/ formula). Compute the…

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Q: Find the slope of the graph of f(x) at the point where the graph crosses the r-axis. pe = Find the…

A: Topic:- application of derivatives

Q: Evaluate the following rational function with the following (a, b, c, and d). 5+3x*+4x3-13x2+13x-1…

A: Let's find.

Q: e*+e¯& =x² –2 lim sin² x–x² x→0

A: Given limx→0ex+e-x-x2-2sin2x-x2 If we put x=0, we get a solution of the form 00…