Let f (x) = x and g (x) =|x| be two real-valued functions, O (x) be a function satisfying the condition; [O (x) – f (x)]² + [¢ (x) – g (x)]² = 0. Then, find o (x). %3D

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: (₁ Find the absolute extrema of the function on the closed interval. ƒ(x) = x³ − 12x + 1, [-3,1]

A: An absolute extrema of a function in a given interval is the point at which a maximum or minimum…

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Q: (f + g - h) (x) f(x) = x + 4 g(x) = 2x2 + 2x h(x) = x² + 1 %3D O x2 + 3x + 5 3x2 + 3x + 5 O x2 + 3x…

A: We use the sum and difference of functions to answer the given question.

Q: sup{f(x) + g(x): x e X) < sup(f (x) : x e X} + sup(g(x): x e X) inf{f(x) : x e X} + inf{g(x): x e X)…

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Q: A-Find the local minimum and maximum of f(x)=xe^3x using the first and second derivative test.…

A: for question A see 2nd ,3rd and 4th step. for question B see 5th step.

Q: 3x-1 Find the critical points of the function f (x) = x+6

A: Here the given Any point x is said to be a critical point of the function f(x) if f(x) is not…

Q: Find the critical numbers of the function.…

A: Critical numbers of a function are the numbers for which first derivative is zero or undefined. Now…

Q: Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = ln(x2 + 5x…

A: The given function f(x) = ln(x2 + 5x + 13),    [−3, 1] Differentiate with respect to x…

Q: The function f(x) = 2x³ - 39x² + 216x 3 has two critical numbers. The smaller one is x = and the…

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Q: The function f(x) = 2x3 – 39x? + 240x + 9 has derivative f'(x) = 6x? – 78x + 240. %3D f(x) has one…

A: Given data:   The expression for the given function is f(x)=2x3-39x2+240x+9. The expression for the…

Q: f(x, y) = e-(x²+y²)(3x² + y²) Calculate the extreme values of the function: = e-(x²+y²) (3x²+ y?)

A:

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

A: Given function is, But, Hence,

Q: Consider the function: f(x) = x2 – 4x + 9 Step 1 of 2: Find all critical points of the function.…

A: Critical point: A critical point of a function is the point x0 in the domain where the function is…

Q: Find the critical point of the following function y= -x2 + 2x - 2

A: Given: The function y=-x2+2x-2, To find: The critical point of the given function.

Q: Find all critical points of the function: f (x) = 7x − 2

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Q: the integration of : f(x) = - 2x+4/(x^2+1)(x^2-4).

A:

Q: Find the absolute maximum and minimum values of f(x)= ln(x^2+3x+15) on the interval [-2,1]

A: We find f'(x) using chain rule

Q: Find the maximum and minimum values of the function f(x) = x² – 6.x +7 on the interval [0, 5].

A: It is given that, f(x)=x2-6x+7   , on the interval 0,5We have to find the maximum and minimum values…

Q: x-1' Find the value of the constant A for which the follo

A: Find the value of A

Q: J. (g o h)(x) 8. (h og)(x)

A: As per the bartleby guidelines for more than three question only three has to be solved .Please…

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. f(x)=-2x²+x-1 a) f(0) =-| %3D b) f(-1)=- c) f(-x)=-X- %3D d) - f(x) = | e) f(x+1)=-3 ) f(2x)= -…

A: 1.    fx=-2x2+x-1   a) On putting x=0                         f0=-202+0-1      =-1  b) On putting…

Q: Example: Find the PDE, which has a general solution ø(→,2) = x x =0, where is an arbitrary function…

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Q: A​ once-popular children's doll is slowly declining in popularity. The quartic function…

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Q: 7. Let f(x)=64x² ln (2x) −16x¹. Findƒ(e)-f(€) 2

A: NOTE: Refresh your page if you can't see any equations. . take x=e

Q: Consider the function f(x) = -6x2 + 4x - 4.  Find the critical point, A of the function. At x = A,…

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Q: F(x)=e^2x (3x^2-x)

A: see 2nd step

Q: The function f(x) = 2x³ – 21x² + 60x – 7 has two critical values. The smaller one equals and the…

A: The given function is f(x)=2x3-21x2+60x-7

Q: Find a 4th degree function that has solutions X=-4-2/3 and x=-4+2/3, x=2i and x=-2

A: See the attachment

Q: Find the extreme values of the function f(x) = x3 + 9x² + 5 on the interval x E [-1,3]

A:

Q: Find the linearization of the function at x = 1.* f (x) 2x - 3x + 7 %3D

A: From the given problem:   fx=2x3-3x+7 ; x=1   As we know that the expression for linear…

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 What are the x-coordinates of all local minima and…

A: Given:f(x)= (3x^2)ln(x) , x&gt;0

Q: 0,x1 x+2,x<-1 f (x)= %3D 2,x2-1

A: Interval notation is a way to describe continuous sets of real numbers by the numbers that bound…

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A: The break-even point point occurs when the total revenue is equal to the cost. At that point, the…

Q: Iff(x) = 1 %3D Зх-1 and g(x) = f-' (x), find g' (x). 1 o g'(x) = -, 3x2 o g(x) %3D뉴 1 2r2 1 o g'(x)…

A: Given f(x)=y=13x-1f-1(x):Replace x with y and solve for yx=13y-13y-1=1x3y=1x+1y=x+13x

Q: Find the critical numbers of the function. (Er g(x) = x6 – 3x4

A: To find the critical numbers we first find g'(x) using the power rule

Q: find the absolute maximum and absolute minimum values of ƒ over the interval ƒ(x) = x - 2 ln x,…

A: The given function and the interval is,

Q: The function f(x)=2x^3−42x^2+270x+8has derivative f′(x)=6x^2-84x+270. f(x) has one local minimum…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. ln(x^2+3x+8) in…

A: Given:

Q: Find, if any exist, the critical values of the function. f(x) = a – 16a - 6 Critical Values: x = Pre

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Q: 5. Determine the critical points of the function: f (x) In(x² + 4x + 14) %3D Enter your answer

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Q: nd all the critical points of the function f(x)= ={ x² 23 if x<1 if x ≥ 1

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Q: f(x) : == - x2, with domain [2, +o) %3D

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Q: f(1-3/x)dx3= X +2x/x + C X-2x ex2+1 of X-2x/2 x(1-2/x) +C x(1 לx-

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

A:

Q: V4 - x 8. g(x) = at x = 0 %3D

A: