3) Find the intervals where the function is increasing and where it is decreasing. f(x) = x² - 6x² +4

Q: 3 + 2x² √3+2 x2 O 2x 3 - +C X + + 2x + C x3 23³3³ +0 x³ + 2x + C O dx =

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Q: Use a graphing utility to graph the equation. Use a standard setting. y = x2 − 6x + 5 x-intercept…

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Q: Given the following total revenue (TR) and total cost (TC) functions for a firm, TR = 5820Q +4Q²-20³…

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Q: 10. The y" of y = (2x¹ + 4x³)(3x¹ − x³) is - a. 336x6 +420x5-120x¹ C. b. 336x5 +420x4-120x d. 48x7…

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Q: On your own, verify that the indicated expression is an implicit solution of the given first-order…

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Q: A rectangle is enclosed by the coordinate axes and the line 2y + x - 5 = 0 Determine the length and…

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Q: An open-top box is to be made from a 12-inch by 18-inch piece of plastic by removing a square from…

A: We can find the value of x by using the second derivative test.

Q: 3. Evaluate III 622 dV where G is bounded by r+ 2y + 4z = 8 in the first octant.

A: see below the answer

Q: 4. Which of the following is an exact DE? A. (x²+1)dx-xydy-0 B. xdy+ (3x-2y)dx = 0 C. 2xydx…

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Q: = If f(x) = f'(x) = ƒ'(5) = 4 tan x, then - sin(x)-4 sec² (x) Cos x

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Q: Find the tangent line, in slope-intercept form, of y=f(x) at the specified point. f(x) = - 5 3 2 -1+…

A: Given function, f(x)=5x-3x+2x2f(x)=5x-3x-12+2x-2

Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8   As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: Find the value of k so that the given differential equation is exact. (y³ + kxy4 - 2x) dx + (3xy² +…

A: Given differential equation is (y3+kxy4-2x)dx+(3xy2+20x2y3)=0

Q: Find the vertical asymptotes (if any) of the gr exist, enter DNE.) x³3x² + 4x g(x) = 5x² - 30x + 40

A: g(x) = (1/2x^3-3x^2+4x)/(5x^2-30x+40)  Find the vertical asymptotes?

Q: The graph of a particular function passes through the point (3,4). Its first derivative is 2yy' + 2x…

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Q: Use dx f'[f¹(x)] Let f(x) = 7x³ +6, x20. Find dx x = 195 to find the derivative of the inverse at…

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Q: Determine whether the differential equation . (8x² − 2xy + 7) dx + (4y² − x² + 8) dy = 0 is exact.…

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Q: Find the tangent line to f(x) = ax³ at x = -1. Assume that a is a positive constant. ***

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Q: 2x² + y² +3z² = 1 y² = 4x x² -z² = y 2z = x² +4y² 2x + y − z =1 z = 4y²-x² E

A: We have to match the graph with equation and write name of these shapes.

Q: 2√ty' =√1-y²

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Q: Determine two numbers whose sum is 36 and whose product is the largest possible. 20 and 16 15 and 21…

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Q: S dx (x²+2x+10) ²

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Q: Use the sum and/or difference rule(s) to find the derivative of the following functions: with…

A: We have to find derivative of given function.

Q: Convert 100 dollars to "widgets" (1 dollar = 3.94 widgets) 39.4 O 3940 394

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Q: S 3x+1 -dx x²-x-6 2

A: We know, ∫ dx/x = ln|x|

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 16 dx +8

A: We have to find the integral

Q: Solve cos(x) = - 0.38 on 0 < x < 2π

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Q: 10- There is a rectangular playing field in Alaska Denali Park for a grizzly Bear with an area of…

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: Given z=x²y+3xy, x=sin(2t), y=cos(t), find dz/dt when t=0

A: ddxcosx=-sinx

Q: Evaluate: S O (1+2√√)¹ 2 O (1+2√)¹ +C 8 O 2(1+2√x) + C O (1+2√)¹ - + C 4 (1+2√x)³ - dx +C

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Q: Calculate the value of the following limits algebraically, (if they 2x-1 a) lim x+1 X² 2x²-9x-5 b)…

A: Topic:- application of calculus

Q: Let F(x) = f(f(x)) and G(x) = (F(x))². You also know that f(9) = 7, f(7) = 3, f'(7) = 8, f'(9) =…

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Q: Find the volume of the solid generated if the area bounded by y = = and the x-axis from I x=1 and…

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Q: xample following flow field: Find the acceleration u= 2x² + 3y, v=-2xy + 3y² + 3zy, w= at a point…

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Q: Derivative application question please answer in full detail! A spherical balloon is being…

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Q: Find the value of c for which the area enclosed by the curves y = c - x² and y = x² − c is equal to…

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Q: Find the constant a such that the function is continuous on the entire real line. f(x) = √5x², x ≥ 1…

A: We need to find a.

Q: The graphs of f and g are given. Use them to evaluate each limit, if it exists. (If an answer does…

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Q: Consider the utility of a consumer consuming two goods, the quantities of which are x and y. His…

A: Let's solve.

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: 2. Consider the function F, that assigns x in its domain to x² - 1 F(x) |x-1| In its domain. a. What…

A: The given function is:Fx=x2-1x-1

Q: 6- Find the volume of a solid, use the Cylindrical Shells method, which involves rotating the region…

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Q: 2. Consider the function F, that assigns x in its domain to x²-1 F(x) = |x-1| In its domain. a. What…

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Q: 4. Let v = (v1, v2, v3), w = (wi, w2, w3) be two non-zero vectors not on the same line in R Suppose…

A: answer is in next step. please give a like !!!

Q: Consider the following initial-value problem. 2y″ + 28y ′ + 99y = 0,    y(0) = 2,    y ′(0) = 0 Take…

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Q: Find the average rate of change of from y = x³ - 2x + 3 from 0 to x = 3. -

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Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) t²3t- 28 lim t→7 t-7

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Q: Let V be the volume of the solid obtained by rotating the region above the x-axis and below the…

A: Recall:  V=∫abπf(x)2dx We have a=0, b=6, f(x)=e-x

Q: Decreasing Annuities The second account earned interest for two months, so if the initial balance…

A: