Consider the function ƒ(x) = −2x² + 8x – 3. f(x) has a critical point at x = A. Find the value of A: A = At x = A, does f(x) have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER.

Q: Let f(x) = x(x-4)³. (a) Find the critical number(s) of f. (b) Find the interval(s) on which f is…

A: (a) A critical point is a point of a function where the gradient is zero or not defined (the…

Q: Differentiate. f'(0) = f(0) = cos(0) sin(0)

A: Please see the below picture for detailed solution.

Q: Find the general solution for the differential equation. dv 6- - 12xy - x = 0 y = = 1/2 + Ce=x² y =…

A: Given differential equation:- 6dydx-12xy-x=0

Q: A spherical balloon is being inflated in such a way that the radius of the balloon is increasing at…

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Q: Consider the ellipse 9x² + 64y² = 576. Consider the point P(16,3). Find an equation for both lines…

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Q: Find all the complex roots. Write the answer in exponential form. The complex cube roots of 16+16i

A: Given:  z = 16 + 16i

Q: What is the minimum value of f(x) = x^2 - 8 ln x   on the interval [1,5]

A: To determine the minimum value of fx=x2-8 lnx on the interval 1, 5.

Q: Urves with more than two asymptotes and/or oblique asymptotes: k a) Graph y ==+x and y = X k where…

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Q: (a) Find the linear approximation L(x) of 2 f(x) = x³ at x = 3 L(x) = x = 27. (b) Use L(x) to…

A: The given function fx=x23. To find the linear approximation of fx at x=27.

Q: y' = xy³ (1 + x²)−¹/2, y (0) = 1

A: y'=xy3(1+x2)-12  dydx=xy3(1+x2)-12given  y(0)=1∫xndx=xn+1n+1+c

Q: mine the average rate of change of f(x) = x³. - x over the interval 1 ≤x≤ 3.

A: We will find the required.

Q: A 200-foot cable weighing 5 pounds per foot is hanging from a winch 200 feet above ground level.…

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Q: Consider the following equations. f(x) = √x + 5 g(x) x+5 Sketch the region bounded by the graphs of…

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Q: Solve the equation y" +4y= S(t-4π), y(0) = 1/2, y'(0)=0

A: The given differential equation: y''+4y=δt-4π, y0=12, y'0=0

Q: Evaluate the iterated integral **²y³ dady.

A: K=∫04∫016x2y3dxdywe know ∫xndx=xn+1n+1+c

Q: a) lim x-0 9+x-3 x

A: The solution is shown below-

Q: Suppose that a company's sales volume y (in thousands of units) is related to its advertising…

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Q: =f* √7t + 10 dt. The arc length function for a curve y = f(x), where f is an increasing function, is…

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Q: The functions describes the distances from the origin at time t of an object in rectilinear motion.…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: If n(A) = 2, n(B) = 5, and n(A U B) = 7, find n(A n B). Need Help? Read It

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Q: Find the distance between the skew lines: x = 5+7t, y=3+7t, 2=8-9t x = 1-t, y = 6, z = 5+8t NOTE:…

A: The given skew lines: L1:  x=5+7t,  y=3+7t,  z=8-9tL2:  x=1-t,  y=6,  z=5+8t

Q: Solve the equation for x given that 1 ≤ x ≤ 8: ln x = sin x, using 5 iterations of Newton's method.

A: To find the solution of the following equation ln x = sinx by using Newton's method For the…

Q: 7. Find dy fo dx for x³ -y + y² = 4.

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Q: Find and simplify the derivative of f(x) = ln(cosh (ax))

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Q: Suppose that f (x, y) = x³y². The directional derivative of f (x, y) in the directional (-3, 3) and…

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Q: Let y = f(x), where f(x) = (5x² + 6)1/3. Find the differential of the function. dy =

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Q: As you move through the first gate, you can see another gate not far in front of you. You approach…

A: Given: g(x) = x+3x2-9 The function does not exist when their denominator is zero. That is,…

Q: Every year, Danielle Santos sells 59,200 cases of her Delicious Cookie Mix. It costs her $2 per year…

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Q: 31. The surface area of an inflating weather balloon is described by A(x) = 4x² - 1 where x is the…

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Q: Determine if Rolle's Theorem can be ap- plied to f(x) = x² + 3x - 18 x + 3 on the interval [-6, 3],…

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Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

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Q: The domain of origin that satisfies the function f(x)= (x)/(x+2) is.

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Q: Find the derivative of the function. -7x³ - 6 6x² +7 f(x)=

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Q: Let f(x) = 7x sin(x) cos(x). Evaluate f'(x) at x = ³7. ƒ'( ³ ) =

A: I have appended the formula used in the solution part of the question

Q: 3. Use the limit definition of the derivative to find f'(x) for f(x) = 7x² + x.

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Q: 6. y =√1+√8x-1 y 1$)+ (x-1) ¹4 y'= 1 + 7. y = [(x-1)(2x³ +1)]¹0 8. y = (4x²-1)³ (5x³ + 2)*

A: 5

Q: Find the limit. sin(8) lim 0 0 90 + tan(0)

A: It's in a 0/0 form, so we can apply L'hopital rule.

Q: you have 2 . DU also can you do explain the integration by part showing what you are integrating

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Q: he area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1- cos 0).

A: We have to find the area of the given cardioids.

Q: 98. Determine whether the vectors AB and PQ are B(-2, 2, 0), where A(1, 4, 1), equivalent, P(2, 5,…

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Q: Find the exact absolute maximum and absolute minimum of h(t) = cos(2t) + √3 sin(2t) on [0,1]. Show…

A: h(t)=cos(2t)+3sin(2t)for critical points, put h'(t)=0d dt(sint)=costd dt(cost)=-sint

Q: Find the derivate of the functions of at any Use the form f'(c) = lim f(x) - f (c) for a and b X->(…

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Q: A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and write…

A: given shaded region is between concentric circles with radius r=8 and r=10. So, it is better to use…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(xy)…

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

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Q: Calculate the derivative of the function. HINT [See Example 3.] h(x) = 3[(6x − 1)(x − 1)]−1/3

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Q: An open-top rectangular box is being constructed to hold a volume of 350 in³. The base of the box is…

A: Given: volume = 350 in³ base material costing = 6 cents/in² front cost = 12 cents/in² remainder…

Q: Solve the differential equation y` = (196+ y)²

A: The given differential equation is: y'=196+y2

Q: 1

A: We have to simplify and write in x according to the given information.

Q: If x² + y² - 3xy² = -1, find dy/dx in terms of x and y. Using your answer for dy/dx, fill in the…

A: Given equation:- x2+y3-3xy2=-1