Find and classify the extreme point of the function f(x, y) 3y2x + x³ - 3y3 - 3x? + 2.

Q: Find the absolute extrema of the function on the closed interval.                         f(x) = 2x3…

A: We find the critical points by solving f'(x)=0 -1 is not in the interval [0,3] 1 lies in [0,3]

Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: The graph of the linear function f(x) passes through the point (x, y) = (1, m), where m is the slope…

A: Given:Graph of f(x) passes through the point (x, y) = (1, m), where m is the slope of the line.

Q: Find the local extreme values of the function ƒ(x, y) = xy - x2 - y2 - 2x - 2y + 4.

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Q: Find the critical point for f and then use the second derivative test to decide whether the critical…

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Q: Examine the function f(x, y) = −3x² - 4y² + 15x - 8y + 5 for relative extrema.

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Q: Find the points of discontinuity of the function f(x)={1−x2,x<0x+2,x≥0 if they exist.

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Q: B. Find and classify the extreme points of function f(x, y) x* +y-4xy-1.

A: Maxima minima of two variables function

Q: Sketch the curve of f 3x y = f(x) = r³ – 8

A: Given,  y = fx = 3xx3-8  We have to sketch the curve.

Q: Find the the stationary points and the local extreme values of the function f(x, y) = −2x/x2 + y2+1

A: The objective is to find the stationary points and the local extreme values for the function…

Q: Determine and distinguish the stationary values of the function f(x, y} = x² – 6x² – 8y². -

A: We need to find the stationary value of f(x,y)=x3-6x2-8y2   For that first we need to find the value…

Q: What is the domain of the function f(x, y) = x² /ỹ – In(x)?

A: topic -  function domain and range

Q: Determine critical points of the function f(x)=∣∣x2−4x+3∣∣.

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Q: Find f'(2) if y = f(x) is the nonnegative function defined for x, y > 0 by the equation x" = y?.

A: To find f’ (2), if y = f (x).

Q: Show that the function f(x,y) = x³ + y³ – 63(x +y) + 12xy is maximum at (–7,–7) and minimum at…

A: Given function: fx,y=x3+y3-63x+y+12xy Formula Used: D-Test: For each point a,b where fxa,b=0 ,…

Q: Examine the function f(x, y) =-3x-4y+15x - 16y + 6 for relative extrema.

A: Here we have to find relative maximum.  The solution is in both 1st and second steps.

Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: Find f-(-1,1) of the function: f(x, y) = x + xy +2a°y?

A: Let's find.

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: Differentiate the function. y = (3x- 2)² (1 –x³)² dy

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Q: Find and classify the critical points of the function f (x, y) = 16x³ – 12x2 + 12xy? + 3y?

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Q: f(x, y) = /4 – x² – y² + V1 – x? -

A: To find the domain of the function, f(x,y)=4-x2-y2+1-x2

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: Find the maximum and minimum values of f(x, y)=x+3xy2-3x2-3y²+4.

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Q: The function f(x,y)=/26-2x²-y² is continuous at point (2,-3). .A False .B True

A: A function is continuous at a point if after putting the point in the function yields a positive…

Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x+2y=5.

A: Given Function f f(x,y)=14-x2-y2 on line x+2y=5We need to find the maximum value For the line…

Q: Find the absolute maximum and minimum of the function  f(x)=xe-x on  the interval [-1,1]

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Q: 2. Find an equation and sketch the graph of the level curve of the function f (x, y) = 16 – x² - y2…

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Q: Find the absolute extreme of the function on the closed interval y = 3cosx ; [0,2π]

A: To find the absolute extreme of the given function.

Q: Find the maximum and minimum values of the function f(x,y)=2x^2+3y^2−4x−5 on the domain x^2+y^2≤9.

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Q: Find the extreme values of the function f(x; y) = x2 + y2 + xy on the curve x2 + 2y2 = 1.

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Q: Find the absolute extrema of the function on the closed interval.                        f(x) = 7x2…

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Q: Determine the stationary values of the function z = x3 – 6x² – 8y² and distinguish between them

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Q: Suppose that f(x,y,z)=x^2yz−xyz^3 is a function of three variables.

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Q: Find the point on the graph of f(x) = Vx that is closest to the point (5, 0). (x, y) =

A: Use distance between point concept and then differentiate

Q: Find the absolute extrema of the function on the closed interval. f(x)=x3+6x2, [-6,1]

A: To Determine: Find the absolute extrema of the given function on the closed inteval.…

Q: Consider the function f(x, y) = x² + xy - 5x- y+1. Then:

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Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x + 3y = 10.

A: Solution of given question is written in below steps.

Q: Find all the stationary points of the function f(x,y) = x3e-(x^2+y^2).

A: Given:

Q: find the critical point and classify the function f(x,y) =xlny +x2 -4x-5y+8

A: Answer

Q: В. Find az if z = f(x, y) is implicitly defined as a function of x and y for the equation below…

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Q: B. Find and classify the extreme points of function f(x, y) = x + y - 4xy-1.

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Q: Find the critical and inflection points of the function f(x) = 4sin³x – 3cos²x

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Q: Find the global extrema of the function f(x)=3x4−6x2+2 on the interval [−2,2]

A: Global extrema of a function exists at critical points or at the end points of the interval.…

Q: Determine all critical points for the function. y = 4x² - 128 x

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Q: The range of the function y= 16-x2 is the interval [0, 0)

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Q: Consider the function f(x, y) = 4x² – 8y² subject to the condition x + y = 25.

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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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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.