Show that given functions are orthogonal on the indicated interval. f1(x) = ex,   f2(x)= xe-x - e-x ; [0,2]

Q: Find all critical points for the function f(x) V(x2 - 4). %3D

A: Given function f(x)=x2-4  To Find all critical points of the given function.

Q: Give Three Functions  of Wronskian ?

A: To Give: Wronskian of three functions.   Wronskian:

Q: Find the perticular number or orthogonal trajectories of x2+cy2=1 passing through the point (2,1)

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Q: Find the critical points of the function f(x) = x³ + 1¹5 x² + 50x + 8. Use the First Derivative Test…

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Q: Find the average rate of change of the function f(x)=−2x2+6x+8f(x)=-2x2+6x+8, on the interval…

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Q: Find max and min of function on the interval    f(x)=-x4-x3+5x2-4 on [-2,1]

A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval. y = √x, [9,…

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Q: Find aa and bb so that the function f(x)={4x^3-3x^2+5, x<-2         {ax+b,             x is…

A:

Q: Find the values of a and b such that f(x) = x³ + ax² + bx + 5 has x = 1 and x = 2 as critical…

A: The function f(x)=x3+ax2+bx+5 has critical points at x=1 and x=2

Q: Find a point c satisfying the conclusion of the MVT for the given function and interval: y = ex − x,…

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Q: The derivative of the function f(x) = 25 x3 -6 x2 +7x- 88 at X = 3 using a step size of 0.5 and…

A: on solving we get

Q: Find all critical points of the function f(x) = x4 – x-

A: Critical point is 5/4 Explanation is given below

Q: Find the linear approximation of the function at the given point. f(x y) = 4x²y3 at (-9,7) O A. L(x,…

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Q: The function f(x) = −2x³ + 3x² + 36x has two critical points, c₁ and c₂. Find them and use the…

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Q: Find linearization L(x) of f (x) = Vx at a =4 and use to approximate 7.8.

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Q: Suppose that z = f(x, y) is implicitly defined as a function of x and y. Determine for 4x²z³ - 5yz²…

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Q: Find the minimum and maximum of the function in the specified interval. 1. f(x) = x² - 6x + 9 on…

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Q: Compute the derivative of f (x) = x 1/3 using the limit definition.                            (x +…

A: Given: fx=x13 To Find: The derivative of the given function using limit definition

Q: Find and classify the stationary points of f(x) 2x} + 4x,x3 – 10x,x, + x}

A: Given,     f(x)=2x13+4x1x22-10x1x2+x22

Q: Find the orthogonal trajectories of the functiony x + ce which is passing through (-2,0)

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Q: Suppose we have a function z = a > 0. f(x, y) = -x² – y² + a(x +y) where a is exogenous and a.…

A: The given equation is z=fx,y=−x2−y2+ax+y Where a is exogenous and a > 0.

Q: find the critical points of f (x) and use the Second Derivative Test (if possible) to determine…

A: Here we will apply first derivative and equate it to 0 to get the critical points and then apply…

Q: Find the values of k that make the function continuous. Jk² + 18x, x > -3 f (x) = kx, x < -3

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Q: State why the function 2z2 - 3z + e-z is analytic everywhere.

A: See the answer below

Q: Find the linearization of f(x)=ln(x2-3) at suitably chosen integer near X=2.1. Then use the…

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Q: Locate the critical points of the function f(x) = x + 2x + 6x - 4 and use the second derivative test…

A: We solve the equation f'(x)=0 to find the critical points of the function. If a is a critical point,…

Q: Find the critical points and the interval on which the given function is increasing or decreasing,…

A: We use application of derivatives to solve this problem.

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4x/3 on the interval [0,…

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Q: Find the value of “c” guaranteed by the MVT theorem over the interval [-8,-6] for the function: F(x)…

A: Given function is : Fx=2x3+9x2-60x        -8,-6 To find the value of c.

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: The nearest integer to a=-0.9 is -1 because at this point, we can easily find the function's value…

Q: Find the maximum value of x if f(x)=5 sin x – Using Quadratic Interpolation with a relative error of…

A: Given: If f(x)=5sin x-x610, find the largest value of x. Using Quadratic Interpolation with a 1%…

Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = e−2x ,…

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Q: The interval over which the function f(x) = becomes continuous is %3D x+8 (-3, 0) (-3, 3) (-00,…

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Q: Find the value k that makes the function continuous. kx + 14, х > 2 f (x) = 11x + 2, x < 2

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Q: find a linearization at a suitably chosen integer near a at which the given function and its…

A: (1)Given:

Q: Suppose you are working with a function f[x, y] and you find that f(¹,0) [x, y] ƒ[1, 0]? Why or why…

A: Given: A function fx,y such that f1,0x,y&lt;0 for all points x,y.   To determine: Whether…

Q: Let f and g be the functions defined for x > 0 by f(x) = (Væ)* and g(x) = (Vx)** Which function is…

A: According to the given information, Consider the function f and g defined as:

Q: Find the value of the constant c such that the function f(x)= (x-2)/( (root 4x+1)-3) if x#2, c if…

A: And

Q: Find the linearization of the function at x = 1. * f (x) = 2x³ - 3x + 7 O y = 6 + 1(x - 3) O y = 6 +…

A: Given, fx=2x3-3x+7

Q: Find all critical points of f(x) = 3 + 12x - x² and use the First Derivative Test to determine…

A:

Q: Let f(x) be a function with second derivative of f"(x) = -(5x +11)?(x – 2) Determine the local…

A: When a function's at critical point x , and the second derivative at x is: less than 0, it is a…

Q: Find the critical points and the interval on which the given function is increasing or decreasing,…

A:

Q: Find the specific that h (-3) =7 function satisfies hlx)こ 6-5x+x and

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Q: Find all points c satisfying the conditions of the MVT for the function f(x)=x3−x in the interval…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x−1, [2,…

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Q: (b) Show that f(x) = ln(x + 2) has a unique fixed point in [0, 2].

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Q: find a point c satisfying the conclusion of the MVT for the given function and interval y = x3, [−4,…

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Q: Find the critical points of f(x)=3x^4 -4x^3 +5 and use the first derivative test to determine local…

A: Given,          fx=3x4-4x3+5