35. f(x) = 5x + 6 37. f(x) = x² – 5x + 6 39. ƒ(x) = x(3x – 1)(x + 9) 41. f(x) = x* – 1 30. J (A) 38. f(x) = x² – 2x – 1 40. f(x) = x³ – x² – 2x 42. f(x) = 2- - - V4 – x² In Problems 43–50, find the x- and y-intercepts, if any, of the graph of the given function f. Do not graph. 44. f(x) = x² 46. f(x) = (2x - 3)(x² + 8x + 16) 6x + 5 43. f(x) = ;x – 4 45. f(x) = 4(x – 2)² – 1 %3D x(x+1)(x- 6) 47. f(x) x² – 16 48. f(x) = 49. f(x) = }V4 – - x² 50. f(x) = }Vx² – 2x – 3 In Problems 51–56, find the function f if f (2) = -3 in each case. %3D 51. f(x) = 4x + k 53. f(x) = kx³ – x + 1 52. f(x) = -2x² + kx 54. f(x) = x* + x' + kx² – x – 1 %3D %3D 2x – k 55. f(x) %3D 56. f(x) ES maldor CHAPTER 2 FUNCTIONS

Q: Suppose that as t` the population size approaches a limiting value x. Express x in terms of the…

A:

Q: For example, an antiderivative for y = 2x is x² + 5 because (x² + 5) = 2x = y. However, the…

A: Part a,Given,           Antiderivative of fx=2x2+8x+17.

Q: 1. A company manufactures and sells a televisions per month. If the cost and the revenue functions…

A:

Q: (d) Finally, show that the conditions for the theorem are not satisfied for the initial value…

A: (D) here fx,y=y13 differentiate it with respect to x ∂f∂x=13y-13dydx initial condition y0=0

Q: For a short run production function q=10lnL if L=5 and the wage rate is $3 the extra cost of to…

A: Answer:----.               Date:----3/10/2021

Q: Show that (0, 0) is a critical point of ƒ(x, y) = x2 + kxy + y2 no matter what value the constant k…

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Q: 28. Find the critical points of f(x) = x3 – 3x2 - 3. а. (0,—3)аnd (2, -7) b. (0,3)and( 2,7) c. (0,2…

A:

Q: 3. Find for the simplified general solution of (1 + x³)dy - x²ydx = 0

A:

Q: 2. Identify the iterative function f(x) = x3 – 9x2 – 6 if initial approximation x, = 2.25

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Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

A:

Q: 27The platis that passes through the e Point C672) and contains the lihie メー4-2t)X= 345t) Zと+4t 4. こ

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Q: 11. f(x) = x² + 7x + 10 Opens up/down: Vertex: Axis of symmetry: Solution(s): y-int:

A:

Q: 16. Suppose your factory produces f(x, y) units of a product when you spend x million dollars on…

A: If “y” million dollars spent on capital then “y” units are produced

Q: 3. Find the particular solution of the differen- tial equation: (x² +y² )dy=xydx, given that x=1…

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Q: Find the critical points of the function f(z) = 3z - 9z.

A:

Q: Suppose we have a function z = a > 0. f(x, y) = -x² – y² + a(x +y) where a is exogenous and a.…

A: The given equation is z=fx,y=−x2−y2+ax+y Where a is exogenous and a > 0.

Q: (4) The general solution to 7xy" – y + 10y = 0 is y = Ax x + x+ +В х + x+ x²+ x³ + and converges on…

A:

Q: 1. Find all critical points and investigate the type and stability of each. x' = xy - 2 y' = x - 2y

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Q: Goes through (0, -2) and has a local maximum at (1, 3) f(x) = 5x² - 10x - 2 O B) f(x) = -5x² + 10x +…

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Q: 5. The function h(x) = x² + bx² + d has a critical point at (4, -20). Determine the constants b and…

A: This question is related to the application of derivatives.

Q: Solve for Elimination of Arbitrary constant given problem is x^2y=1+cx

A:

Q: 1. Find the critical points for f(x) = 3x5 – 20x3.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What happens when you try to approximate V3 by using fixed point iteration of g(x) = 3/x?

A: To determine what happens when 3 is approximated using fixed-point iteration.

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A: An explicit solution is any solution that is given in the form y=y(x)

Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a>0 see below the answer and calculation

Q: What is the value of the coefficient d of the equation y = ax + bx² + cx + d so that it will have…

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Q: Suppose that a political campaign by Loki estimates that the candidate’s polling percentage y and…

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Q: The function f(x) = x^3 + bx^2 + c has a critical point at (-2, 6). Determine the value of b and c.

A:

Q: 2y – x = 3t y+ x' = 3et 3e-t x (0) = y (0) = 0 3s2 L (x) = (s+1)(s–2)(s²+1) 3(2s3 –s–1) s2…

A:

Q: 8. Use the fact that the critical points of f(x, y) are found when vf(x,y) = 0 to show that (-3,-2)…

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Q: 3. x - y=t + 3 4. x = VT-T; y =t- 3t 5. x = vE + 2; y = t² - 3

A:

Q: x² + y² F(x, y) =- - is a homogeneous function of degree

A: For finding degree of homogeneous function, Put x=hx and y=hy

Q: 14. Show that f(x) x+4 never intersects its horizontal asymptote. %D 3x+1

A:

Q: If f(x) = x - ka 1 has a relative maximum at r = -2, then the value of k is

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Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

A:

Q: 9. The total cost and total avenue, in dollars, from producing x couches are given by C(x) = 1000(x²…

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Q: d. If x=c is an inflection point for f, then f(c) must be a local maximum or local minimum for f.…

A:

Q: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: Find the solution to the initial value problem as an explicit function of the independent variable.…

A: Given : (t2+1)y'+y2+1=0,   y(3)=2

Q: 1. Determine the nature of the stable points of the function f (x, y) = x²y – x² – 3xy + 3x + 2y –…

A:

Q: s(x,y)=ex^2+y^2 How do I find the critical point of this function.

A:

Q: Solve the initial-value problem for yy as a function of xx. (64−x2)dydx=1,y(0)=5(64-x2)dydx=1,y(0)=5

A: (64-x2)dydx=1⇒dy=dx64-x2integrating,                ∫dy=∫dx64-x2+c      [c=…

Q: In a certain company, the income from the sale of x thousand pieces of products is given by I (x) =…

A: We first try to find the profit function.  Profit= Income - Cost…

Q: Let y : R → R be the real-valued function defined on the real line, which is the solution of the…

A: The differential equation is given as Y’  = -xy + x , y(o) = 2 From the type of the problem we can…

Q: 1)Classify the critical points of the function f(x,y)=x²+y³+x²y+4

A:

Q: Number 29. Find the derivative of the function. I'm confused with the simplification part at the end…

A: Obtain the derivative of the function as follows.

Q: If f(x)=x* and g(x)= x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule multiplies derivatives to…

A:

Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.