Given h(x) = x3+bx2+cx+d, h(x) has a stationary point at x=2, an inflection point at x=-1, and a y-intercept at 5. Determine values of b, c, and d

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: and the net is decribed by the equation y = V1 – x2 – z2, y 2 0,

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Q: Show that the relation y^2 - x^3 + 8 = 0 implicitly defines a solution to the nonlinear equation…

A: The given data is: y2-x3+8=0

Q: In the given question , find d2y /dx2 implicitly in terms of x and y :-   xy - 1 = 2x + y2

A: In the given question , find d2y /dx2 implicitly in terms of x and y :- xy - 1 = 2x + y2

Q: Find the relative maximum and minimum values. =x2 + y² - 6x + 12y - 9

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Q: If y = f(x) is the solution of y' – 3y =-12.e 9z, f(0) =1, then

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Q: Given that f(3) -2 and f'(3) = 4, estimate f(3.5) using a linear approximation.

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Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) 2y³ + 3x² = C (F) 2y³ + x³…

A: Introduction: An orthogonal trajectory of the family is any curve that cuts each member of a…

Q: +] has the general solution u(x, y) = e"[f(x)+g(y)] where f and g g are arbitrary functions

A: ∂2U∂xdy+∂u∂x=0let U(H.Y)=e-yf(x)+g(y)

Q: find the point at which the line g(x)=−1x+0g(x)=-1x+0 intersects the line k(x)=−4x+9

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Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: : Find the orthogonal trajectories of the family of curves y4 = kx³. (A) ³ + 3x² = C (B) 2y³ + 2x² =…

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Q: Find real-valued closed formulas for the trajectory x(t + 1) = Ax(t), where [-0.8 A = -0.6 -0.8] 0.6…

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Q: Use variation of parameters to find the particular solution to y'' - 7y' +12y = 3e³t Y(t)= Preview

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Q: In(ax) f(x) has a stationary point at Find a and b. bx 2' 3e,

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Q: The y, of y'"-y=2x2-x -3 by using variation of parameters is: .A Y,(x)= x - 1 .B y,(x)=x² + x +1 .C…

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Q: Use variation of parameters to find a particular solution of y"- 2y' +y = 14xie" Yp(x)

A: y''-2y'+y=14x32ex find the roots for the homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real…

Q: Find the relative maximum and minimum values. f(x.y)= 8xy-x - 4y

A: Given :f(x,y)=8xy-x3-4y2

Q: 1) Find the equation of the curve whose slope at any point p(x,y) is m = (x * +16x + 4)²(x ³ + 4)…

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Q: Find the value of x and y which satisfy 2x + 3y = 8 and whose product is a minimum.

A: To solve the following problem

Q: 8. For the graph of the linear function H(z) = -4z + 3, the slope is %3D and the y-intercept is

A: Consider the given equation as Hz=-4z+3

Q: Use variation of parameters to find a particular solution of y"- 2y' + y = 14xie Yp(x) =

A: Auxiliary equation for the given equation:

Q: Use variation of parameters to find the particular solution to 3t y'' + 5y + 4y = 2e Y(t)=| Preview

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Q: Find the relative maxima and minima of y by the second-derivative test: (a) y = -2x2 + 8x = 25…

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Q: The population density of a city is given by P(x,y) = - 25x - 30y + 500x + 240y + 180, where x and y…

A: Population density is given by following function  P(x, y) = - 25x2 - 30y2 +500x + 240y + 180

Q: Use variation of parameters to find the particular solution to y'' + 5y' + 4y = 2e-34 Y(t) = […

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Q: Find the relative maximum and minimum values. f(xy) = e 6x2 + 4y2 + 8

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Q: Determine the point(s) at which ƒ(x) = x3 - 12x has a horizontaltangent line

A: The points where the tangents are horizontal are the points at which slope is zero.That means,…

Q: 2. Determine C when x-y%3D0 show the solutions. (xy + x)dx = (x²y2 + x² + y2 + 1)dy

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Q: Find the linearization of y=2^x at a=0

A: use derivative to find the Linearization of y

Q: d. perpendicular to the line y – 3x = 6, and has a y-intercept of -2. e. parallel to the line 2x +…

A: we have write an equationin the form: y= mx+b            → (1)Given line Y-3x=6⇒ Y = 3x+6 which is…

Q: Find all the local maxima, local minima, and saddle points of thefunctions ƒ(x, y) = 2xy - 5x2 - 2y2…

A: Given;      f(x,y)=2xy-5x2-2y2+4x+4y-4 Let us first to find partial derivative  ∂f ∂x=2y-10x+4 ∂f…

Q: Find the orthogonal trajectories of the given family of curves x^2 + y^2% D c^2. *

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Q: Find the equation of orthogonal trajectories of the given function 8x² + y² = c.

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Q: Given that y1 = 3x is a solution of æ°y" + xy' - y = x2 on the interval (0, 0), use the reduction of…

A: Concept - used the reduction of order

Q: Given that g(2)=5 and g'(2)=3, linearize g(x) near x=2 and use this linerization to approximate…

A: Consider the linearization formula for g(x) near x = a.

Q: Find the relative minimum f(x,y)=288y2+x2-x2y

A: According to the given information it is requires to find the relative minimum of the function:

Q: Find all the local maxima, local minima, and saddle points of thefunctions ƒ(x, y) = 2xy - x2 - 2y2…

A: The given function is fx,y=2xy-x2-2y2+3x+4. This implies that, fx=2y-2x+3fy=2x-4yfxx=-2fyy=-4fxy=2

Q: As a result of urbanization, the temperatures in Paris have increased. In 1891 the average daily…

A: Average temperature is calculated by the total sum of temperatures divided by number of observations

Q: Find the optimal values ​​of the function f (x, y) = 4xy + 5. Subject to the restriction x ^ 2 + y ^…

A: Consider the objective function as fx,y=4xy+5 subjected to restriction equation x2+y2=18. Let the…

Q: With y=c1.x2+k curves and curves x2+2.y2-y= c2 intersect perpendicularly. Where C1 and C2 are…

A: Given two curves are y=c1x2+k   and x2+2y2-y=c2  , where c1 & c2 are arbitrary constants. Let us…

Q: The time (in hours) that a branch of Amalgamated Entities needs to spend to meet the quota set by…

A: T(x, y)=x4+16y4-32xy+43Tx =4x3+0-32y(1)+0Tx=4x3-32yTxx =12x2-0Txx =12 x2Ty…

Q: If the function f(x, y) = ;x³ + y² + 2xy – 6x – 3y + 4 has one saddle point (a, b), then 46 + a = -

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Q: Find the equation of a line parallel to x = -8+ 2y that passes through the point (8, –2). Oy = -x –…

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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: 4. Determine the minimum value of the function y = f(x) defined implicitly in the equation x² + 3xy…

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Q: Find the relative maximum and minimum values. f(x,y) = x² +y2 +4x- 12y

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Q: Find the standard (slope-intercept form) eq at the specified points. 1. f(x) = 3x² – 12x +1 at…

A: 1) Tangent line of the function f(x) at x1,y1 is given by y=f'x1x-x1+y1  3x2-12x+1 at P(0,1) x1=0,…

Q: For what values of m does Y = emx satisfy Y" + Y' - 2Y= 0 ?

A: For what value of m does Y=emx satisfy Y''+Y'-2Y=0

Q: Use variation of parameters to find the general solution of y" – 2y' + 5y = e'.

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