Let the function f(x) = |x + 1| – |2 x – 1| %3D - 1.simplify the expression of f and draw representative curve 2.by graphically deducing(without calculation proof) the point f is not derivable and the solution of f(r) > 3

Q: The orthogonal trajectories of the family of curves y = cx² is A x=ky² B C x²+2y²=k 2x² + y² = k

A: We have to find the

Q: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

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Q: What is the relative minimum value of the function f(x, y) = x³ – 3xy + y³ – 2?

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Q: Calculate the linearization L of f(x) : 5e* at x = 1. x2 Express your answer in terms of e and x.

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Q: 4. For the below function, find the stationary point (s) and prove if a maximum, minimum, or saddle…

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Q: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1 + kx.

A: The given function is

Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

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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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A: Given that  f(x) = ax2 + bx has an absolute maximum at the point (1,2).

Q: Given f(X)=−xe^x whats the root of the linearization of f(x) at a = 4.3?

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Q: Consider the function f (x,y) = x³ – 3xy + y³. Find all critical points of f and determine whether…

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Q: Find the linearization L(x)of the function at a .

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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 all points (x, y) on the graph of g(x) = 1/3 x3 - 3/2 x2 + 1 withtangent lines parallel to the…

A: Given: The function gx=x33-3x22+1, To find: All the points x,y on the graph of given function at…

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

A: Here we use Taylor's approximation.

Q: 3. Find the linearization L(x) of the function at a. F(x) = Vx, a = 4

A: Use the formula for the linearization of a function about any point.

Q: The function F(x) = 2x^3 + 3x^2 has a relative minimum point at x =

A: We will solve the problem

Q: Find the local linear approximation L (x)of the function f (x)= x² +3 at x = 1

A: Given that: f(x)=x2+3

Q: 8. Find the extremum and saddle points of the function f(r, y) =r' - 3ry + y if any.

A: Due to Bartleby guidelines, only 1st question can be answered if multiple questions have been asked.…

Q: 2. Show that the function u p(xy) + Vry (y/x) provides the equation = 0.

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Q: Find the linearization L(x)  of the function f(x)=x^3/4  at x=16

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Q: Find the linearization L(x) of the function f(x)=x^3/4 at x=1

A: Given, f(x)= x³/4 x=1 Therefore, f(x=1)=1³/4 f(x=1)=1/4

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 linearization of the function given below at the specified p f(x) = 4 In(x) at a = 1 L(x) =…

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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: b. Find the orthogonal trajectories for the family of curves x² + y² =C².

A: we have to find the orthogonal trajectory of the given family of curve

Q: Find x' for x(t) defined implicitly by x+t°x+t -8=0 and then evaluate x' at the point (-2,2).

A: x3+t3x+t4-8=0Differentiate w.r.t…

Q: Consider the function f(x,y) - x-44x- 4y and determine if, at the point (4,0) if the function is a…

A: Note: Since you asked multiple questions I solved one. For solution of other problem please post the…

Q: True or False: The linear function y = mx + b , where m ≠ 0 has no maximum value on any open…

A: true, the function y = mx +c has no maximum value in any open interval Reason: the graph of y = mx+c…

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: (a) Find the linearization of the function f(x) =x+ at x= a=1

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Q: Find the extreme values of the function f(x; y) = x2 + y2 + xy on the curve x2 + 2y2 = 1.

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Q: Find the linearization L(x) of f(x) at x=a. f(x)=x/2x+9 a=0

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Q: (12) Find the local maximum, minimum and saddle points (if any) of the function f(x, y) = x3 – 3x +…

A: Local maximum or minimum of the function

Q: + A(- for 0<x< 1, then u attains its maximum in the interval 0 sxs1 either at x=0 or at x= 1.

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Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: If f (x) - 2x - kex has a relative maximum at x = -2, then the value of his

A: Given  f(x)=2x-k.exNote: As there is no h in the equation it is assumed that we need to find…

Q: 1 Find the length of the curve f(x) + from x = 2 to x = 4. %3D 6. 2x

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Q: Find a multivariable function f(x, t) that satisfies the Black-Scholes equation: ft = f - xfx -…

A: f(x,t)=etlog(x) satisfies Black-Scholes equation: ft = f - xfx - x2fxx

Q: Find the linear approximation L(x)of f(x)=x^4 at the point a = −5 L(x)=

A: Given that f(x) = x4 We have to find the linear approximation L(x) of f(x)=x4 at the point a= -5.

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

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Q: 7 For the function eX, the linear approximation around x = 2 is %3D

A:

Q: Find the linear approximation 0 to Write your answer in the form y = Ax + B. at x =

A: Explanation: The Linear Approximation should be a line that can substitute (in a narrow interval)…

Q: 4. Determine the constant a,b, c, and d so that the curve defined by f(x) = ax³ + bx² + cx + d has a…

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Q: Show that the linearization of f(x) = (1 + x)k at x = 0 is L(x) = 1+ kx.

A: We need a linear approximation formula for f(x).

Q: 1. Any function y = f(x) can be expressed as x = f(y) in standard mathematical methods for solving…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find the extremum and saddle points of the function f(x, y) = x³ – 3xy + y³ if any.

A: Given problem is :

Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,