10. If the minimum of the function y =x 2-4x+21 occurs at x = 2, what are the coordinates of the minimum point?

Q: 8. What is the minimum value of the function defined by y = cosx + 4? В. З A. 2 C. 4 D. 5

A: Given- y=cosx+4 To find- The minimum value of the expression.

Q: 2. Find the critical points and determine whether they are a maximum, minimum or neither. y = a° –…

A: In the question we have to find the critical point also max. and min. points.

Q: Find the absolute minimum value of the function g(x) = e*/(9x), x > 0.

A:

Q: What is the set of approximate y-values of the relative minimum and maximum of this graphed…

A: Given the graph

Q: Suppose f '(x) =x4+x³– 6x². Determine the value of x where f has a relative minimum value. A x=2 (B…

A: f'(x)>0 - then f(x) is increasing f'(x)<0 - then f(x) is decreasing

Q: 1. The sum of two positive numbers is 10. Find these numbers if the sum of their squares is a…

A:

Q: Find the minimum value of x²+y² + z²,

A:

Q: For what value of x the function x2+y2 is minimum if x+y=20

A:

Q: 8. What is the minimum point of the given function y = x² – 6x + 10? B. k = -3 A. k = -1 C. k = 1 D.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose f'(x) =x++x³ – 6x². Determine the value of x where f has a relative minimum value.

A:

Q: Suppose f'(x) =xr++x³– 6x². Determine the value of x where f has a relative minimum value.

A: F''(2)  greater then 0

Q: Find the absolute minimum value of the function f (x, y) = 2x² + 2y? subject to the constraint 9x2 +…

A:

Q: If f'(x) = x - 2x² - x +2, thenf has a relative minimum at x= 1 -1 2 -2

A: The answer is

Q: Find the minimum point for the curve y = x- 4x -1.

A:

Q: If 2x +y= 10, find the minimum value of x+ y2

A:

Q: Minimize g=10x+9y Subject to 4x+y≥19   2x+y≥13 x+4y≥24 x≥0 y≥0 What is the minimum value and at…

A:

Q: z = x? + xy + y² - y

A:

Q: The graph of  f(x) = 2(x − 2)2 − 7 is a parabola that opens upwards with its vertex at (x, y) = 2,−7…

A: Consider the graph of f(x) = 2(x − 2)2 – 7

Q: Q4:- Find the minimum value of the function f(x, y) = x + y, subject to the constraints xy = 16 , x…

A: Please see the explanation below

Q: 23. Find two numbers whose sum is 10 and the sum of their squares is a minimum.

A: Let the two numbers be  x and yx+y=10⇒y=10-xx2+y2=SS=x2+10-x2   =x2+x2-20x+100   =2x2-20x+100

Q: Find the minimum value of the function z=9x+2y subject to the following constraints. XS11 ys12…

A: According to question given that:Function z=9x+2yx≤11y≤123x+y≥183x+7y≥54

Q: Suppose f'(x) =x4+x3– 6x2. Determine the value of x where f has a relative minimum value.

A: Explanation of the answer is as follows

Q: Determine the critical value(s) of y = -8x2+ 12x + 3 and state if it is relative minimum or relative…

A: For critical point. Put dy/dx =0. Put the value of critical point in given equation to find critical…

Q: 1. The graph of f(x) = 2x3 + x² – 20x + 1 has a relative minimum at A. x = -2 C. x = 2 D. x = 1 ק…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 1. The minimum point on the graph of the equation y = f(x) is (2, – 1). If f(x) is shifted 3 units…

A: Given that y=f(x)minimum point on the graph is (2, -1)

Q: Determine the maximum and minimum points of the given functions below. h(z)=4z3−3z2+9z+12

A:

Q: 1. The Maximum point of y = (x²+2x+10) (x-3)

A: Find out the maximum point.

Q: 1. The product of two numbers is 147. If the sum of one of the numbers and thrice the other is to be…

A:

Q: Determine the extremum points and the values of the maximum and minimum of the function + f(x, y) :…

A: Given:  f(x,y)=xy+yx;   g(x,y)=x2+y2-8=0So,…

Q: x² minimum point of y х + 5х — 4 %D х — 5

A: Given equation is y2=x2+5x-4x-5 taking square root of above equation y=x2+5x-4x-5 Now…

Q: If y =4√x- x the value of x that maximizes y is ......... and this maximum is

A:

Q: If f'(x) = x - 2x´ - x + 2, then ƒ has a relative minimum at x= 2

A:

Q: Find the local maximum and minimum values and saddle point(s) of the function x² y² – 8x + y f(х, у)…

A:

Q: f(x) =Vx+4 entify the minimum values of the function above when 5 < x 12.

A: Given query is to find the minimum value of the function for the given interval.

Q: Express y = 3x2 – 8x - 1 in the form y = 3(x – p)² + q, where p and q are constants and hence find…

A: To express in the form y=3(x-p)²+q

Q: Find the absolute minimum value of the function f(x, y) x+ 4y2 = 9. 2x + 3y subject to the…

A:

Q: 01. What is the point of the minimum of the function y = 4x? + 4x – 15? А. (0.5,-16) В.(-0.5,-16) С.…

A: Given:- y= 4x2 +4x –15 Find the point of the minimum of the function Now, Let the point are (x, y)

Q: Find the value for x for which the graph of y =2e reaches its first minimum value.

A: To find the value for x for which the graph of below equation reaches its first minimum value.…

Q: 2) Use DESMOS to graph Y = 10* + 3, show critical points. %3D

A:

Q: What is the minimum of the function y = –x° + 3x for x < -1? O 2 O-4 4 O-2

A: We can solve it graphically. Graph of f for x&lt;=-1:

Q: 1- What is the relationship between minimum point and convex function?

A: As per our guidelines we are supposed to answer only one question.* *Kindly repost other question as…

Q: A financial department of a company has arrived at the following Cost and Price function p(x) =…

A: At Break Even Point (BEP) cost and prize are equal (means profit Z = P(x)-C(x) is zero) We have…

Q: Suppose a company has fixed costs of $32,000 and variable cost per unit of 1/3x + 444 dollars,where…

A: It is given that,

Q: Suppose the labor cost​ (in dollars) for manufacturing a camera can be approximated by…

A:

Q: If f'(x) = x³ – 2x² – x + 2, then f has a relative minimum at x

A: f'(x)=x3-2x2-x+2, we have to find relative minimum of f.

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.