The function f(x) = 2x° – 36x2 + 162x – 11 has two critical numbers. The smaller one equals and The larger one equals

Q: Find the critical point(s) of the function. S(x, y) = 4e²-}+4y

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Q: Determine the coefficients of the equation y-ax'+bx²+cx+d so that it will have critical points at…

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Q: Minimize f(x) = x² + 54 ; using Interval halving method for 2 ≤ x ≤ 6. E= 10-³

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Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

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Q: One of the critical points of f(x,y) = x³ – 5y² + 10y – 27x is:

A: The given function is fx,y=x3-5y2+10y-27x. The critical points of a function f(x, y) are obtained by…

Q: Find the critical value Zα/2 that corresponds to α=0.15

A: From the given information:The significance level is α=0.15,Therefore, confidence level is 1- α =…

Q: Find the value of a so that the function f(x) = xe has a critical %3D point at x = =D3. NOTE: Enter…

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Q: Find the critical points of the function f(x, y) = 8y³ +12x² – 24xy and classify them as local minin…

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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 extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Given that,

Q: Find the critical numbers of the function. y-4 g(v): y2 - 2y + 8

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Q: particular

A: We find particular solution.

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

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Q: Consider the R² – R function f defined by f (1, y) = 2² – 6x +3y² - . (a) Find all the critical…

A: For critical points we need to find first order partial derivatives of given function and substitute…

Q: Find the critical numbers of the function. y- 2 g(y) = %3D y2 - 2y + 4

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Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

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Q: Let f(x) 18xe 18 %3D (a) f'(x) : (b) Solve f'(x) 0 to determine the critical values of f.

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Q: Find the best linear approximation to f(x) = x² on the interval [0, 2].

A: Here we use Taylor's approximation.

Q: Find the critical numbers of the function. y-4 g(v) = y2 - 2y + 8

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Q: Use variation of parameters to find a particular solution of the ODE y" – y = 2e".

A: Given differential equation is  y''-y=2ex we have to find  the particular solution of this…

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

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Q: Find the solution (varition of parameter)   X2y11-2xy1+2y=x3sin x

A: According to the given information, it is required to find the solution of the given differential…

Q: Determine the value of the Wronskian W(y1, y2) of y" - 2y + 1 = e2*(x + 1) if x-0.2 by using…

A: Given, y''-2y'+1=e2xx+1. The objective of the problem is to obtain the value of the Wronskian if…

Q: find the critical numbers of the function

A: Firstly, we find h'(t) for given function h(t)

Q: 6. Locate the absolute extrema of the function H(x) = - x* Inx on 1 3 2' 2 Give exact solutions.

A: We have to find out absolute extrema

Q: Find the critical point of the function: f(x, y) = 4x2 + 2y2 − xy + x

A: we have given a function f(x, y)  We have to find the critical point

Q: A) Find and classify the critical points of f(z, y) = x³ + y3 – 6y? – 3.x + 9 using the first and…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Draw the particular solution for y= f (x) given the initial condition f (-1) = 0.5 x Clear Undo…

A: Given data is : f-1=0.5 To draw the particular solution for y=fx

Q: 9. Let f(x) = x³ – 3x² + 3. a. Find the y-intercept of the function; b. Find all critical points of…

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Q: Find all stationary (critical) points of the function g(x, y) = x³ + y³ + 3x² + 3y + 3x + 3xy +1.

A: First calculate the partial derivatives, gx, gy  for g(x,y) . Solve the equations, gx=0 , gy=0…

Q: f (x, y) = -2x – 4.xy + 2y? + 2x – 2

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Q: Find and classify the critical points of f(x,y) = 4r+20² - y²

A: Find and classify the critical points of f(x,y)= 4x+2x2-xy2.

Q: Find the linear approximation to f(x) = (x+2) at 0 and use it to approximate (2.001)

A: Given :           f(x) = (x + 2)5 at 0 To find :             The linear approximation of f(x)…

Q: The function f(z) 2x-36z+120z-8 has two critical numbers. The smaller one is x = and the larger one…

A: A critical point is a point in the domain of the function where the function is either not…

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

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Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: Find the critical point (xo, yo) of the function f(x, y) = 2x2 + 2xy + y? + 2x – 3.

A: Consider both the image for the solution.

Q: Find the critical point/s of the function f(x,y) x³+2xy-2x-4y

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Q: (b) Find all stationary (critical) points of the function g(x, y) = x³ + y³ + 3x? + 3y + 3x + 3xy +…

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Q: Suppose that the function f(x, y) = x°y+ax – 8y + 5 has a critical point at (2, –2). What must the…

A: For a function of two variables, f(x, y), a critical point is defined to be a point at which both of…

Q: 3. Find a linear approximation to the function at the point x = 3. y = f(x) = x²e + 8x

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Q: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

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Q: Find the critical point (x0,y0) of the function f(x,y)=120x+120y−xy−x2−y2

A: A point (a,b) is critical point of function f(x,y) if either ∂f∂x(a,b)=0 and ∂f∂y(a,b)=0 or atleast…

Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

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Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

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Q: 1. Find and classify the critical points of f (x, y) = 6xy – 4x³ – 3y?

A: Critical points of f will occur: fx and fy is o. Given equation is f(x,y) = 6xy-4x3-3y2…

Q: The value of Wronskian of two functions y, =7* and y2 =7** is

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Q: 1. Explain how would you determine the maximum value of y= 1 3-cos x

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Q: Use variation of parameters to find a particular solution of y'' - Y = 4e-x 1-e-2x Yp (x) =

A: Solution of the differential equation, By using the method of Variation of perameters

Q: 25 p1 3) Compute f(x)f'(x) dx where f(x) =x +2, using the Composite Trapezoidal 2 rule, your results…

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