5. Given the function of two variables (a) find the critical points (b) find the discriminant, D(x, y) (c) classify each critical point as a local maximum, local minimum, or saddle point S(x,9)= =x'-4x+y* -10y

Q: 5. Use the second derivative test to classify any critical points of f(x, y) = x²+2y²-x²y and…

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Q: Find the maximum point of y = x + x a. (2,-2) b. (1,2) c. (-1,-2) d. (2,3)

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Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

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Q: Given f(x,y) = y² - 2xy² + 2x² - 2x + 1. Identify all critical points and at each point (using…

A: extreme points  of the function fx, y=y4-2xy2+2x2-2x+1Rule: ∂ ∂ xxn=nxn-1,

Q: g(a,b) = a²b-2a² - 4a + 2ab. Determine all the critical points of g. And determine the relative…

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Q: 2. Examine the function f(x,y) =x² - 15xy +y +7 for relative extrema and saddle points. a. saddle…

A: Please see the explanation below

Q: 8. Locate all points where f(x,y)=x* +3x²y-y has a Relative Minimum, Relative Maximum, or Saddle…

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Q: ve test to identify any critical points a these. -2 – 6y² + 12x - 36y – 87

A: In this question, the concept of maxima and minima is applied. Maxima and Minima The critical points…

Q: 10. Use the second derivative test to classify the critical point(s) of the function ƒ (x, y) = x³ —…

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Q: find the local maximum and minimum values and saddle points of the function f(x,y)=9(x-y)e-x^2-y^2

A: Given fx,y=9(x-y)e-x2-y2. Now,…

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.