1 For a function f(x), we have f(x) = 1+ x? and f(0) = 0 prove that x +y f(x) +f(y) =f 1-xy

Q: What is the critical point of the function f (x) = cos x? 2. What is the maximum point of the…

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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…

Q: The function f(x) = 2x 30x + 126x – 6 has two critical numbers. %3D The smaller one is x = and the…

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Q: Find the local and/or absolute maxima for the functions of the specified domain. Y= 1/(x-x^2) over…

A: Here we have to use the concept of derivatives. Here we use second derivatives test for finding…

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: 6. Find the absolute maximum and absolute minimum of the function f(x)=x´e^ +1 on the…

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Q: 3) The function f(x) = e*(x² + x - 1) has derivatives f'(x) = e* (x2 + 3x), f"(x) = e*(x² + 5x + 3),…

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Q: 7. Find the absolute maximum and absolute minimum values of f(z) = 2x – 3r2/3 on the interval…

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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: Xs-1 Let f(x) = {[x+1]-[1-x). -1<x<1 x21 1x|x- where [] denotes the greatest integer function, then…

A: Introduction :

Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

Q: 2. Find the local maximum and minimum values and saddle points (if any) of the function f(x, y) = xy…

A: Here, the given function is: f(x,y)=xy-2x-2y-x2-y2

Q: 3. GIVEN: ƒ(x): 2x2 – 3 xs2 (8x-11, x>2 DISCUSS THE DIFFERENTIABILITY OF THE GIVEN FUNCTION AT x = 2…

A: Given query is to determine whether f(x) is differentiable at x=2 or not.

Q: 11.  Let h(x) = x^4 − 2x^2 + 3.(a) Find all critical points and use the First Derivative Test to…

A: Given information:The given function is shown below:

Q: (a) Find the critical numbers of the function f(x) = x6(x – 4)2. (b) What does the Second Derivative…

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Q: 1. Find the critical points of the function f(x, y) = x² + 4xy. 2. Find the local maximum and…

A: As per guidelines we can answer only one question at a time, so if you need more answers kindly…

Q: Use algebraic methods to determine the critical value(s) of f(x)= x/(x^2-x-2). Give your answers in…

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Q: 3. Use Rolle's Theorem to show that the function f (x) = x² sin(x) – x sin(x) has a critical point…

A: For y = f(x). Let f(x) is continuous at every point of the closed interval [a, b] and differentiable…

Q: Find the critical numbers of the function. 3. g(x) = V 25 – x2 X =

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Q: (5) Find the local maximum and minimum values of f(r) = 1+3x2 – 2.r using either the First…

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Q: 3. Use derivatives to find the critical points anc (a) f(x)= x³ – 9x2 + 24.x + 5

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: . (a) Find the critical numbers of . f (x) = x 4 (x -1 )3(b) What does the Second Derivative Test…

A: (a) We say that x=c is a critical point of the function fx if fc exists and if either of the…

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: Find equations of the tangent lines to the curve f (x) = (2x +1)/(4x−3) that are perpendicular to…

A: Given,            f(x) =2x + 14x - 3

Q: 5. Find the maximum and minimum values of the function f(x) = x e-2a on the interval [0, 1].

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Q: 1 Find the derivative of g(x) = Vx-1 Find f'(x) and f"(x) of f(x) = 11x³.

A: Here we have to find the derivatives of the given function.

Q: f (x) = x² – 3x/3 [0,2]

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Q: A quadratic function f(x) = x + 3 x2 + 2 x + 3 has an inflectional tangent y = 3 x + 3 at (0,0).…

A: Given:- A quadratic function f(x) = x3+3x2+2x + 3 has an inflectional tangent y = 3x + 3 at (0, 0).…

Q: Let f(x) = x(1 + e*) -e*. 1) Verify that the function f(x) = 0 has solution in the interval [0,1].…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: 2. f(x) = x^3 − 27x (a) Use the derivative of the function f(x) to find all critical points. (b)…

A: f(x) = x3 − 27x For critical points, f'(x) = 0 ∴f'(x) = 3x2 - 27 = 0 =&gt;3(x2 - 9) = 0 =&gt; x = ±3…

Q: a)Use the second derivative test to determine whether the function has a local maximum or local…

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Q: 17 The function f is defined by f(x) = 5x - c, where c is a constant. In the xy-plane, the graph of…

A: Solve both the problem in the following way:- (i) given point will satisfy the function. (ii)…

Q: Q 3) Find the critical numbers of f(x) = x4(x - 1). Derivative Test' tell you about the behavior of…

A: given information function

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: 1. Find all the critical numbers of the function (Justify Your Answer) (a) [5Vx – 2 f(x) = x > 2…

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Q: What is the critical point of the function g (x) = (x ^ 2/2) + x (ln (x) −1), using Newton-Raphson,…

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Q: Q.4. locate the critical points of the function f(x) = x²(x-1)³ and identify critical points which…

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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: Find the absolute maximum and minimum vaules of the funct ion g(x)= (x^2-3x+4)/(x-1) on the interval…

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Q: 3. The horizontal asymptote(s) of f (x) = Vx² – 1- væ² +x.

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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: 2. Given: f(x) = 4x³ + 6x² – 72x – 9 (a) Verify f(x) has critical points at x = 2 and x = -3. (b)…

A: Given :

Q: 2. Find all critical numbers for the function: g(x) = x/2x +1 B. 0. ÷.글 1 1 А. - - | 2 3 2 c. - D.…

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Q: 1. For the function f(x) = 2x3 - 3x2-36x restricted to the interval [-4,4], %3D (a) Find the…

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Q: Consider a differentiable function f with domain R and derivatives f'(x)=-aebx(1+bx) and…

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Q: The function f(x) : (2х — 6)е has one critical number. Find it. - x =

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Q: The derivative of the function f is given by ƒ'(x): = e¯* cos(x²), for all real numbers x. What is…

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Q: Find all critical points for the function f(x) = (z² – 4) . %3D

A: To find the critical points of f(x), find the derivative of f(x) and equate it to zero.

Q: 3(a): Find the critical points of the function f(x) = 3x² – 6x. (b): Apply Rolle's theorem for the…

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