You have given a function A : RR with the following properties (z € R, n e N): A(n) = 0 , X(x+1) = (z), A(n+;) = 1 Find two functions p, q : R +R with q(x) # 0 for allz such that A(r) = q(x)(p(x)+ 1).

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

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Q: What is the value of a such that the function y = 2x4 - ax² + 3 has twin global minima at x = -3 05…

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Q: The function f(x) = 2x° - 36x + 192x 8 has two critical numbers. %3D The smaller one is x = and the…

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Q: The function f(x) = 2a – 392? + 240x – 4 has two critical numbers. The smaller one is x = and the…

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Q: 2. Find and classify the critical points of the function f (x, y) = 6x2 – 2x³ + 3y? + 6xy

A: The solution is given below in the next step:

Q: The critical points of the function f(x, y) = x³ + xy + y² are _____.

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Q: he average cost function is defined in economics as C¯(x)=C(x)x, where C is the cost of…

A: Given:  C(x)=0.01x3−0.4x2+13x+400,

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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 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

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Q: Are the f-llowing functions Continual s OFC メーE X-2 スト=メ 1P 2) FCX)s X- S X +7 at XE-1 X5qXs (xフゴ

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Q: The critical points of the function f(x) = 36a – 2a4 occur at z= 0, z = +3.00 x = 0, x=±12.00 O r=…

A: We have to find critical points

Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings​ (in…

A: given S'x=150-x2C'x=x2+114x where S'x is the rate of annual saving and C'x is the rate of annual…

Q: NOW IT'S YOUR TURN ! Find the critical points of the following functions : 1) f ( x ) = -3 x3 + x 3)…

A: f(x)=-3x13+xfirst differentiate both sides with respect to xf'(x)=-3×13x13-1+1f'(x)=-x-23+1for…

Q: Show that f(x) = ln xn /x is a decreasing function for x > e and n > 0.

A: Given function is, But, Hence,

Q: The function f(x) 2x – 33x2 + 108x – 1 has two critical numbers. The smaller one is x = and the…

A: Explained below

Q: 1. Find and classify all critical points of the function f(x, y) = x² + y²-3x - 4y.

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Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

Q: 4. Find and classify the critical points of each of the function f(x,y) = x² + y² + 3xy.

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Q: The function f(x) = 2x – 45x + 300x – 5 has two critical numbers. The smaller one is x : %3D and the…

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

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Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

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Q: The function f(x) = 2x 30x2 + 126x 1 has two critical numbers. - The smaller one is x = and the…

A: Solution: the objective is to find the critical numbers of the given function

Q: 1 Find the linearization of the function f(x) = 5x+4 atz-1.

A: The given function fx=15x+4 at x=-1

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: Determine all critical points for the function. f(x) = x3 - 12x + 3 x = -2 and x = 2 Ox = -2 O x = 2…

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Q: The critical points of the function f(x) 36z2 - 2x occur at 2- 0, r +4.00 0, z +2.40 %3D I0, z -…

A: We have to find the critical points of the function f(x)=36x2-2x4.

Q: 7. The critical points of the function f(x) = 1³-272 are (a) ±3 (b) ±1 (c) +√2 (d) 1

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 5 Find the point X to minimize the function f(x1, x2) =1+¤1 +2x2+ from the strating point X, = using…

A: We are given the following optimization problem : f(x1 , x2) = 1 + x1 + 2x2 + 5/x1 + 10/x2 And we…

Q: The function f(x) = 2x° – 27x² + 108x – 5 has two critical numbers. The smaller one is x = and the…

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

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Q: A. Find and classify all the critical points of the following function: F(x,y)=(3x +4x)( y²+2y)

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Q: Find the critical points of the given function. a) f(x)=√x²-4 b) f(x)= |3x +21-1

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Q: 2 If f(x) = 2x- kr has a relative maximum at r = -2, then the value of k is %3D

A: Note :-  If f(x) has relative maximum at x=a then f'(a) =0.

Q: Consider the function f(x, y) = e-xy It is possible to state that f reaches global extremes (global…

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Q: 4. The function f(x) = x³ – 6x² + 9x – 4 has a relative maximum at (A) x = 0 (B) x = 1 (C) x = 2 (D)…

A: Let f(x) = x3 - 6x2 + 9x - 4 Suppose the function has critical point at x = c then If f'(x) > 0…

Q: The function ff has a continuous second derivative, and it satisfies f(1)=2f(1)=2, f′(1)=0f′(1)=0…

A: Given: f(1)=1, f'(1)=0, f'(1) = 2 A critical point of a function occurs when the first derivative…

Q: 1. Consider function f(x,y) for which = 24x² + 114y and %= 114x + 24y2. Wbich of the points (5, 5)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The function f(x) = 2x³ − 42x² + 270x – 4 has two critical numbers. The smaller one is x = and the…

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Q: Suppose that f(x, y) = e e-x² - 2y² + x Then the maximum value of f is

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Q: (b) Find the linearization of function S(x) = Vx V220 at a=216 and use approximate number (c)Find…

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Q: Find the critical numbers of the function. b. g(x) = V1- x² %3!

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A: Given that number of advertisements in circular = x number of advertisements in news papers = y…

Q: Find the absolute maximum and minimum values of f(x) = e * – 3x on [0,5].

A: f(x)=ex-3x Take derivative wrt to x f'(x)= ex-3

Q: 1)Classify the critical points of the function f(x,y)=x²+y³+x²y+4

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Q: The graph of f​(z​)=16^z passes through the points (−1,x ), (0,x)and (1,x) simplify

A: The equation of the graph is given that: f(z)=16z. So, when it passes through the points (-1,x), it…

Q: 3. Consider the function f(x) = r - 1+x 1- a. Explain why, when evaluated in a floating point…

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