Let f(x)=x* + 2x' – 3x² – 4x +4. Find: (a) the critical numbers of f (x); (b) the points at which f(x) has a relative maximum or minimum; (c) the intervals on which f(x) is increasing or decreasing.

Q: Find all critical points of f(x,y) = 1/x - 1/y + xy and classify each as a relative minimum,…

A: We use second order partial derivative test to find relative maximum and minimum, saddle point

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Q: Given the function f(x) = (x+3)²(x-1). Find the critical points of f(x) and its increasing and…

A: f(x)=x+32x-1f'x=x+32ddxx-1+x-1ddxx+32       =x+32+2x-1x+3       =x+3x+3+2x-1      =x+33x+1to find…

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A: To Determine: Find the critical points of

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Q: 5. If c is a critical point of F(x), when the is a local maximum or minimum at c? Explain

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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: Consider the function f(x) = 648x¬² + x³. Taking the initial point as x = 6 and increment value as…

A: Here, fx=648x2+x3 Take x0=6 and △=1 Iteration 1) k=0 of xk Now, xk+1=xk+2k△ Here, x0=6…

Q: Find absolute maximum and minimum points, if they exist, of f(x)=x^3+x^2-X+1 on the interval…

A: We need to check value of f(x) on critical points and boundary values of interval to find absolute…

Q: 8. Identify all critical points of f(x, y) = 6xy-x - y and classify each as an appropriate relative…

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Q: Find the critical point of f (x, y) = 3x² + xy - 5x + y°, and determine its nature.

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Q: (b) Let f(x) = 12x35+ 15x* – 40x³ + 17. Find the critical numbers, and show what the Second…

A: f(x) = (12x 5+15x4 -40x3 +17.   critical points   f'(x) = 0   60 x4 + 60x³-120x²  = 0.   x² ( 60…

Q: In the function:  f(x)= (3x^2)ln(x) , x>0  What are the critical numbers of the function?

A: Given function is

Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: Find the critical numbers of the function. f(x) = 5x In x %3D X =

A: The given function,  fx=5x ln x

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A: For critical points put f'(x)=0.

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A: To find: The minimum and maximum value of the function on the given interval by comparing values at…

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Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x-2x²

A: We can use application of derivative order to solve the given problem.

Q: Find the critical numbers of the function. f(x) = x³ + x?

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Q: Find all FIRST and SECOND order critical POINTS for f(x) = (x² +x – 2)'/3

A: fx = x2+x-213f'x = 13x2+x-213-1 . ddxx2+x-2        = ddxx2+ddxx+ddx-23x2+x-223        =…

Q: 3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a)  Find f"(x).   (b) Then use…

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Q: Find the x-coordinates of all critical points of the given function. Determine whether each critical…

A: Differentiate the given function with respect to x and equate it to zero,…

Q: b- find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x²

A: Points of local extremum can be calculated by using the first derivative. These are points which…

Q: Find and classify all critical points of the function f(x, y) = x+2y-In(x¹3³)

A: Given :f(x,y)=x+2y4-lnx4y8

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Q: Find the critical points of the function x + 1 f (x) = (5 – x)² -

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Q: Find all the critical points of the function f(x, y) = e" (x² + y²) and determine whether each of…

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Q: 6. Find all critical points of f(x, y) = 2y4 + x2 – 6xy and classify each critical point as a local…

A: Given function is fx,y=2y4+x2−6xy Differentiate fx,y=2y4+x2−6xy partially with respect to x, we get…

Q: 4. Find all of the critical points of the function f (x)

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Q: have critical points at x=2 and x--2 f(x) = x² + 4x + 4

A: Critical points:x=2 , x=-2

Q: Approximate the critical points of g(x) = x cos−1 x and estimate the maximum value of g.

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Q: Let f(x) = -2x' +3x² +1 on Find the critical numbers for y = f(x), and show how you use the Closed…

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Q: Find the critical numbers of the function

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Q: What value of a makes ƒ(x) = x2 + (a/x)have a local minimum at x = 2?

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Q: Find all the critical points of the function f(x, y) = x³ + y³ – 9x2 – 21x – y - 66 and label them…

A: Local Extremum values:              Consider the function f(x,y) .For critical points , fx(x,y)=0…

Q: construct a suitable Liapunov function of the form ax2 + cy2, where a and c are to be determined.…

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Q: Determine the critical point/s of f(x) = ln(x2 + 4x + 14) on [-4, 2]. ΟΧ -- -2 Οχ -3

A: Given, f(x)=ln(x2+4x+14) on -4,2 We know that, if a is a critical point of the function if f'a=0.

Q: Find the critical points and the intervals on which the function f(x) = (x³ – 4x) e* + 15 is…

A: given f(x)=x3-3247xex +15 we have to find the critical points and the intervals on which the given…

Q: Consider f(x) = 1/x on [1,∞). Find all the critical points. Is there a maximum? If yes, find it. If…

A: here, objective is to find  the critical points of the function f(x)=1/x on [1,8)

Q: Find the minimum and maximum values of the function y = 8Vx² + 1 – 7x on the interval [0, 8] by…

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Q: Find the critical points of the function x + 1 f(x) = (5 – x)2 -

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Q: 8) State the critical points of the function k(x) = x2 In x2.

A: Given,          The function kx=x2lnx2

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A: Given: fx=x3+ax2+bx fx has a local minimum at x=4 . fx has a point inflection at x=1 . Since fx…

Q: The functions f(x, y) = x 2 + y 2 and g(x, y) = x 2 - y 2 both have acritical point at (0, 0). How…

A: We have f(x, y)=x2 + y2 and g(x, y)=x2 - y2 By finding the partial derivatives fx=2x, fy=2y, gx=2x,…

Q: ind the x-coordinates of all critical points of the given function. Determine whether each critical…

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Q: Find the critical points for the function: f(x,y)=x3+y3-9x2-48y-3 and use the Second Derivative Test…

A: To determine the critical points for the function and classify the critical points.

Q: a) Determine the critical points of f (x) = x - cos x, for xe[0,2m). b) Use a sign line to describe…

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Q: find thr critical numbers of the function f(x)=1/3x^3-4x^2+12x+2

A: Consider the function