Given that f(x)= x³+ ax2 + bx has critical numbers at x =1 and x = 3,then a,b are O -7,8 O -8, 7 none O -9,6 -6, 9

Q: 1. Answer the following question? Let f '(x) = (x – 3) (x +4)(x² + 1). What are the critical…

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Q: 3. Let f(r, y) = y²x – yx² + xy. Find all critical points of f.

A: We have to determine critical points of f

Q: 14. The set of all critical numbers of f(x) = 2 cos x + sin 2x on (0, 2n) is B. {등, 똥) 5T A. . В. c.…

A: f(x) = 2cosx +sin2x for critical point derivative of function is 0 f'(x) = -2sinx + 2cos2x -2sinx +…

Q: Prove that f (x, y) = (x + 2y)e*y has „no critical points.

A: Consider fx,y=x+2yexy. The critical points of two variable function exist at the points where both…

Q: Find and classify all the critical points of f(x, y) = (x - 1)y2 - x3

A: Let's find.

Q: 1. Prove that for all x, y ER, max (x, y) = x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y}=-

A: What is minimum and maximum Value: For a given set of numbers, the minimum value of the set is the…

Q: In Exercises 1-2 find the critical numbers of the given function. 1. f(x) = x²V2 – x 2. f(x) = cos…

A: We need to find the critical numbers for each of the given functions.

Q: 3) Consider the autonomous DE: y' = y² + 3y - 10 A) Find the critical points of the given DE.

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Q: If (2/3,1/6) is a critical point of f(x, y) = x² – In(x)+ xy-2y2then (2/3,1/6) is:

A: A critical point (a,b) can be classified as a point of local minimum, local maximum or saddle point…

Q: 1. Let f(x, y) = x³y+ 12x² – 8y. Find all critical points of f.

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: The critical Points of f(x, y) = x3 – 3x + 3y? – 6y are: None of these O (1,-1) and (1,1) O (-1,1)…

A: Partially differentiate with respect to X and Y and equate with zero. Solve both equation and get…

Q: Determine the critical value of x2 with 1 degree of freedom in each of the following…

A: a) The level of significance is 0.01.

Q: 8. Find and classify all the critical points of f(x, y) = 4x²y+2xy² - 6xry.

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Q: a Find all critical points of z = (y- 3)(z+ 2y+ 7), = (y+z). Show work.

A: We have to find the critical points of the given equations. For the critical points find the…

Q: The critical value of t at a given alpha level will be smaller than the comparable critical value of…

A: Solution-: The critical value of t at a given alpha level will be smaller than the comparable…

Q: Let f(x) = (7+ 3x)* f(x) has one critical value at A = For x A, f(x) is Select an answer v

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Q: Given f(x)=6*x^3+6*x^2+-4*x, identify the two critical values. Put the most positive critical value…

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Q: The critical number(s) of f(r) = (x+ 1)/3 is (are)

A: Given,        The critical numbers of fx=x+113

Q: 1+ By using the definition In(1+x) = / 1 -dt, show that for a certain range of values of r, t…

A: Solution:

Q: Let f(x) = (7 – 2x)" f(x) has one critical value at A = For x A, f(x) is Select an answer

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Q: 2- Max z =30 x, + 30 x2 X +2 x2 2 80, 3x +2x2 2 120, Simppler s.t. X, X, 20

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Q: Let p(x) = x2/x+2 and p'(x) = x2+4x/(x+2)2 (a) Find all critical values for p(x). Show you work.

A: We have to find

Q: What are the critical points of Cobb-Douglas production function  q=K^0.2L^0.6 subject to…

A: First nwe have to change the required equation from 2 variables to a single variable.

Q: 1. Let flxx) = x³ + y3 - 3x2-3y2 - 9y. (a) Find all of the critical points of f.

A: Part (a): (i) Find derivative of x and y. (ii) Equate to zero, to get critical points.

Q: If (1,1) is a critical point of f(x,y) = x³ – 3x + 3y² – 6y then (1,1) is:

A: (1,1) is the local minimum point   explanation is given in below step

Q: 5. Let f(x) = ax'+bx²+cx+d. Determine the values of a, b, c, and d if f(x) has a point of inflection…

A: f(x) = ax3 + bx2 + cx + d  Point of inflection is (0,4)  So, f(0)   =   4  i.e.    a(0) + b(0) +…

Q: 4Vo Find the critical points of S(x) = x² +

A: Given Sx=x2+4V0x

Q: Let f(æ) = (6 + x)" f(x) has one critical value at A = For x A, f(x) is Select an answer

A: Find the critical value as f'(x)=0

Q: Let f(x) = (3 – 4x)² f(x) has one critical value at A = For x A, f(x) is Select an answer

A: We have to find the critical point

Q: Suppose that the average cost, in dollars, of producing a shipment of a certain product is 20,000…

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Q: (1) Find all critical points. (a) ƒ(x,y) = x³ – y3 – 2xy + 6

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Q: Find the critical points of f(x) = x'e X. .3.-X O A. X =0 and x = 3 O B. X = 3 only O C. X = 0 only…

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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: 15. Let f(x) = x² -4x+3. What are the critical number(s)? x = 1 b. x = 3 c. x= 1 and x 3 a. d. x = 2…

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Q: 2. Given f(x) = x' + ax² + bx has critical numbers at x=1 and x=3, find a and b. .2

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Q: One of the critical points of f (x,y) = x3 - 5y2 + 10y-27x is: O (1,-1) O (3,1) None of these O…

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Q: Suppose (1, 1) is a critical point of f. In each case, what can you say about f? (a)     fxx(1, 1)…

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Q: 1. Prove that for all x, y ER, max (x, y) x+y+lx-yl 2 x+y-lx-yl 2 and min (x, y)=-

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Q: 2. Find and classify all the critical points of f (x,y) = 2x – 9y – xy + x² + 5y².

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Q: Find all critical points of f(x,y)=3x2+5xy+4y2.  If there are multiple critical points, separate…

A: to find:- critical points.

Q: The critical Points of f(x, y) - x' -3x +3y2-6y are: None of these O (1,1) and (-1,1). O (01) and…

A: We will find the first order partial derivatives of f and equate them to 0 to find the critical…

Q: 1 3 4. The set of critical numbers of f(x)= 3 x3 + 3 are 1)AO 0, (-/3,/3) BO CO {3,3-} {0,1} 1/2

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

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Q: The critical Points of f (x, y) = x³ - 3x +3y2 -6y are: O (-1,1) and (1,1) O (1,1) and (1,1) O None…

A: It is given that, f(x, y)=x3-3x+3y2-6y   Critical points of 2 variable function are the point where…

Q: 8. Find and classify all the critical points of f(x, y) = 4x y+ 2xy - 6xy.

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Q: One of the critical points of f(x,y) = x³ – 5y² + 10y-27x is: None of these O (1,-1) O (3,-1) O…

A: The point (a, b) is a critical point (or a stationary point) of f(x, y) if any one of the following…

Q: If f" (c) > 0 where c is a critical number of f' (x), then (c, f (c)) is a relative maximum of of f…

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Q: x2/3 is (are) The critical number(s) of f(x x – 1

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Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: 35. Suppose that the volume, V(x), of a box with a square base and an open top satisfies the…

A: topic - critical points of functions