Suppose plane P contains the points A(5,0,-1), B (2,3, 2), and C(-2,1,–4), and assume P, is the tangent plane to a function z = f(x,y) at the point A. Find a %3D possible formula for f(x, y) that is NOT linear (there are many correct answers!).

Q: #8. In each case, sketch the set of points determined by the given conditions (a) /2-1+i/>1 (b)…

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Q: 6. There equations. are two line through (-2,0) tangent to the parabola y = 4r. Find their

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Q: Evaluate Sr. (0, 2- z2).d along each of the following paths: (a) the line from (1,-1) to (1, 1), 固助…

A: Integration

Q: 10. Determine whether the function is linear, constant, or neither y - 12 = 0 OA OB Dc A) Linear B)…

A: Topic - Functions We are given y-12=0

Q: 2. Construct the cubic spline that intersects with function f(x) at these points (1,-5), (0,3),…

A: Given Data: To construct the cubic spline that intersects with function  at the points , ,  and use…

Q: 3) Find the distance from ( − 11 , − 8 ) to ( 1 , − 13 ).

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Q: Find the distance from the point (-3, 2, -4) to the plane 5x + 5y - 4x = 3.

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Q: 5. How many lines are tangent to both of the parabolas y = -1-x² and y = 1+ x?? Find the exact…

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Q: 5. By considering lines through the point (-1,0), find all rational points on the ellipse x² + 2y² =…

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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.