Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.) f(x) = −x2 + 2x + 1 on [3, 6]

Q: Solve the given differential equation. 3ydx - 3xdy + xdx = 2dx

A: 3ydx-3xdy+x9dx=2dxwe know ∫xndx=xn+1n+1+cd dx(yx)=xdy-ydxx2

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of…

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Q: Consider the right circular cone with a height of h and a base-radius of R, shown below. By…

A: Solution:

Q: π 6x Find the linearization L(x,y) of the function f(x,y) = eº cos (7y) at the points (0,0) and 0,-…

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Q: Let a = (5, 1, 0) and b = (2, – 4, − 1).

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Q: Consider the function f(x) = 12x5 +75x¹ - 120x³ +1. For this function there are four important…

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Q: Assuming 6x³ - 2y² + 4xy = 0 defines y as a differentiable function of x, use the theorem dy = dx dy…

A: To find derivative at given point

Q: J xlnxdx X X

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Q: The tangent to (2,4) on the graph of a function f(x) is y = 5x - 6. Evaluate f'(2). (a) 5 (b) 4 (c)…

A: We have given the equation of tangent line y=5x-6 of f(x) at point (2,4).

Q: has a point of inflection. 2 z = 2 3. r = 0, 4 4. # = 0, -4 g 5. r = 0, 1. Find all values of at…

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Q: 400 gallons of pesticide is accidentally spilled into a lake and uniformly mixes with the water. The…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of pesticide at time t…

Q: Obtain the particular solution satisfying the initial conditions indicated. 2. (t² − x)dt - tdx = 0;…

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Q: Q17 Given P(q) = -2q² + 30q-25 (a) Find the profit from selling the 2nd unit. (b) Use marginal…

A: Given:- Pq=-2q2+30q-25

Q: S Du Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate…

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Q: Use differentials (or equivalently, a linear approximation) to approximate sin(56°) as follows: Let…

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Q: Find the linearization L(x,y) of the function f(x,y)=²x cos (3y) at the points (0,0) and ¹ (0.7) The…

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Q: The temperature in a hot tub is 103° and the room temperature is 75°. The water cools to 90° in 10…

A: Here we apply the Newton's law of cooling

Q: Question 21 Suppose that is differentiable function and f'(r) 2 2r-1 for all are R. If f(0) = 1,…

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Q: When a mass of 2 kilograms is attached to a spring whose constant is 32 N/m, it comes to rest in the…

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Q: Suppose that f is differentiable at 1 and f'(1) = 1 = f(1). Evaluate lim xf(x²+x-5)-16 22-4 (Hint:…

A: Given f is differentiable at 1 f'(1)=1=f(1) We are required to find limx→2x4fx2+x-5-16x2-4

Q: Solve this linear programming problem using graphical methods. Restrict x ≥ 0 and y ≥ 0. Minimize g…

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Q: Find the derivati: (2) g(x)= g'(x) = 25 35+2 (5) 3 2 b) f (x) if f(x) = 5x ² + 6x² - 9 f(s) (x) =

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Q: Find the derivative of the function at the given point in the direction of A. f(x,y) = -6x-9y,…

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Q: Consider the function f(x)= x4-98x² + 11, and an absolute maximum value equal to -6<x< 15. This…

A: Given: fx=x4-98x2+11, -6≤x≤15   Use the Power Rule: ddxxn=nxn-1

Q: Let (5,2,2). P-(1.-2,0). A=(4,3,0) be points in R³. Find the general equation of the plane P in R³…

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Q: 12 1층 1 + du 6

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Q: The area of an ellipse with axes of length 2a and 2b is лab. The percent change in the area when a…

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Q: A simplex matrix is given. 1 10 X = 01 y = 4 5 7 12 12 0 9 0 14 00 The solution is complete, so…

A: We have to find the maximum value of f and values of x,y.

Q: distance in between the point P(3, 1, 2) and the point Q(0, 4,

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Q: For y = f(x) = 3x -1, x = 4, and Ax = 2 find a) Ay for the given x and Ax values, b) dy = f'(x)dx,…

A: according to bartleby policy we do only first part of multiple questions (1)   f(x)=3x-1given  x=4…

Q: Using the equation y= x^3/ x^2 - 4  Determination of the second derivative of the function…

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Q: Suppose a primal minimization problem and its dual maximization problem were solved by using the…

A: We have to find the solution of the maximization and minimization problems.

Q: Find dy/dx at the given point without first solving for y. xy2 125 at (5, 5) d 11

A: The given equation is: xy2=125 Use the Power rule: ddxxn=nxn-1 The Product rule: f·g'=f'·g+f·g'

Q: Consider the center of mass of the following. A lamina occupies the part of the disk x² + y² ≤ 9 in…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y=x and y=2-x…

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Q: du Draw a dependency diagram, and write a chain rule formula for ds Choose the correct dependency…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y) = - 4xy + 5y², Po(-4,1),…

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Q: Find a vector function, r(t), that represents the curve of intersection of the two surface the cone…

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Q: Sketch the region of integration and change the order of integration. So f f(x, y)dydx

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Q: A video store manager observes that the number of videos sold seems to vary inversely as the price…

A: A video store manager observes that the number of videos sold seems to vary inversely as the price…

Q: Find the derivative of the following function: f(x) = ³√x² -2 (a) f'(x) = 3 1/ (b) ƒ'(x) = 3³7x²…

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

Q: At exactly two of the labeled points in the figure below, which shows a function f, the derivative…

A: Given graph:-

Q: 2. Let y 3x23 a) Find the change in y, Ay when x = 5 and Ax b) Find the differential dy when x 5 and…

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Q: Find the derivative of the function at Po in the direction of A. f(x,y) = 5xy - 4y², P (2,10), A=…

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Q: Find all points (x, y) on the graph of y = x2 −6 with tangent lines passing through the point (3,…

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Q: Question 18 ( Show that the equation has exactly one real solution. 207e+2023 In 24

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Q: Evaluate dw dt OA. -9 OB. 5 O C. 11 O D. 7 at t= 1 for the function w(x,y) = x² - y² + 9x; x = cos…

A: Given: w(x,y)=x2-y2+9xx=costy=sint   We are required to find dwdt at t=π2

Q: Suppose that f(x, y) = z²y. The directional derivative of f(x, y) in the directional (-1,-2) and at…

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Q: Find the mass of the solid bounded by the planes x+z=1, x-z = -1, y = 0, and the surface y=√z. The…

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Q: The graph of a function is given. Use the graph to estimate the following. (Enter your answers using…

A: A graph of the function is given, we have to find its domain, range, and increasing and decreasing…