What is the value of the coefficient d of the equation y = ax + bx² + cx + d so that it will have critical points at (1,0) and (-2,27)?

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A: Given The curve ax4+bx3+cx2+dx+k passes through P15,-210, has a critical point at P24,-416 and an…

Q: Solve the separable dr +rtanodo= 0, r(x)=2. equation (initial value problem)

A: givendr+rtanφdφ=0dr=-rtanφdφseparate variables1rdr=-tanφdφintegrating on both side

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A: Given, The expression y=2x2-x4 We have to find the critical numbers of the expression.

Q: 8) Find the family Coff esponding to of orthogonal trajectories y=kx".

A: To find the orthogonal trajectories corresponding to below curve.

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A: Given query is to find the critical points and show its relative maximum or maximum.

Q: critical point of y = xe*

A: Given: y=xex We know that for any given functiony=fx in it's domain, at critical point either…

Q: 7. Solve the boundary-value problem: y" + 3y = 6x, y(0) + y'(0) = 0, y(1) = 0

A: The boundary value problem is y''+3y=6x Subject to y0+y'0=0, y1=0

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Q: Pind the critical point of y=1+hx

A: Given: y=1+lnxx We know that for any given functiony=fx in it's domain, at critical point derivative…

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: What is the solution to the initial – value problem : 4x?y" + 4xy' – y = 0 with y(4) = 2 and y'(4) =…

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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: What is the solution to the initial – value problem : 4x²y" + 4xy' – y = 0 with y(4) = 2 and y'(4) =…

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

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Q: What is the stability of equilibrium points of A and B? Is the energy of B higher than A?

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Q: SOWE FOR THE ORTHO GON AL TRAJECTORIES y² = 4x² (1-ex)

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Q: A manufacturer incurs the following costs in producing x water ski vests in one day, for 0<x< 175:…

A: Given : The manufacturing cost of x vest in one day is given by  C (x) = 0.05 x2 + 25 x + 500 ,…

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Q: Use Euler's method with step size 0.2 to estimate y(0.4), where y(x) is the solution of the…

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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: 6. Find the general solution of Utt2uxt3uxx = 0 and then find the solution of the initial-value…

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Q: 3. Find the critical points of y : e 2x-1

A: The given function is y=e2x-1x To find the critical point

Q: Provide the exact solution of the initial value problemx''  = -x; x(0) = 0,  x'(0) = 1

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Q: 5 4х — 2 d Find dt - dx x² + 20 2 4t – 2 t2 + 20 2 – 16t - 16t2 + 20 16t – 8 ¢2 + 20 2 – 4t - t2 +…

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

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Q: 9. Find the critical points and classify these as local max, local min, saddle point, or "can't…

A: (f) . Given function psf(x,y,2 = (x2+2y2+322)e  (x2+y2+22)solution :-To find the critical pointsfx =…

Q: A manufacturer incurs the following costs in producing x water ski vests in one​ day, for 0<x<200​:…

A: =&gt;c(x)=0.05x^2+15x+245 =&gt;c(x)=0.05x+15+245/x

Q: [1] Determine the orthogonal trajectories of y(1+2x²)=ax.

A: The given equation is:y1+2x2=axy=ax1+2x2              ..............(1) Determine the orthogonal…

Q: If the curve y = ax^4 + bx^3 + cx^2 + dx + e pass through the point (-1, 8), be tangent to the line…

A: Definition used -           Equation of a tangent line -                         y-y1=f'(x1)(x-x1)…

Q: If Z = x + iy than Z is: Z = x - iy Z = -x + iy Option 3 Option 2 Z = x + iy Z = -x - iy Option 4…

A: Explanation of the answer is as follows

Q: Solve the initial value problem. nt 7y – 2y = e-, y(0) = Let a, be the value of a for which the…

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Q: Obtain the particular solution for: 2y" +2y=2sinx y(0)=0, y'(0) =1 By using method of variation…

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Q: Find the critical value z Subscript alpha divided by 2zα/2 that corresponds to alphaαequals=0.18.

A: Introduction: The quantity, zα/2 is the critical value of the standard normal distribution, above…

Q: Solve: sec x = V2 + 2πkk e Z U + 2π시k E Z 3. + 2πkke z 2Tk k EZ 4. 4 + 2rk|k € Z 3 + 2rk|k E Z 3. of…

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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: SOLVE FOR THE ORTHOGONAL TRAJECTORIES X'(3k-x) - ky = xy

A: Take first derivative and eliminate k.

Q: determine the coefficients of the equation y=ax^3+bx^2+cx+d so that will have a slope of 9 at…

A: The equation y=ax3+bx2+cx+d so that will have a slope of 9 at (-1,-4),a critical point at x=2, and a…

Q: Some initial value problems do not have unique solutions صواب ihi

A: Yes statement is true: y(t)=0 for t∈[0,1] and y(t)=(t−1)^2 for t≥1.

Q: 2) Solve the following initial value problem using the method of variation of parameters Yo = 2.

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Q: If Newton's method is used to find the critical number of f(x) = a® – a³ + æ² – 2x with initial…

A: Image is attached with detailed solution.