Locate the critical points of the function p(t) = 4t³ + 3t² - 126t Then determine whether they correspond to local maxima or local minima.

Q: Find the critical point(s) of the function. S(x, y) = 4e²-}+4y

A:

Q: The function f (x, y) = 3x3+y2-9x+4y is given. a) Find the critical points of function f. b)Do…

A:

Q: Find the minimum and maximum value of the function on the given interval by comparing values at the…

A: we have to find the minimum and maximum value of the function on the given interval by comparing…

Q: find the minimum and maximum value of the function on. the given interval by comparing values at the…

A:

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

A:

Q: Find the critical points of the function f(x, y) = 8y³ +12x² – 24xy and classify them as local minin…

A:

Q: Find the extreme values of f(x, y) = x² + 2y² subject to xy = 4 using Lagrange multiplier method.…

A: Here we have to use the Lagrange multiper method

Q: Find the critical point(s) of the function f(x, y) = x^2e^(−x^2−y^2) and classify them as local…

A:

Q: Find the critical numbers of the function. y-4 g(v): y2 - 2y + 8

A:

Q: Find the critical numbers of the function. g(y) = y2 - 2y + 8

A:

Q: Find all the critical points of the function f(x;y)=.x3+y3-3xyDetermine if they are local…

A:

Q: a) Find all critical points of the function f(x,y) = x³ + 3y - y³ - 3x and classify them as local…

A:

Q: Determine the critical points of the function f(r, y) = 4x +4y + x²y+ xy? and whether they are local…

A:

Q: Find the critical numbers of the function. y- 2 g(y) = %3D y2 - 2y + 4

A:

Q: Find and classify the critical points of the function f(x, y) = 4x²y - 2x - y².

A: We need to determine and classify the critical points of the function: f(x, y)=4x2y-2x-y2.

Q: Find the critical points of the function f(r, y) = 8y+ local maxima or saddle points. - 24.ry and…

A:

Q: Find the critical numbers of the function. y-4 g(v) = y2 - 2y + 8

A:

Q: Q2/ Find the orthogonal trajectories of the family of curves x-y - c² YAS

A:

Q: Find the orthogonal trajectories of the functiony x + ce which is passing through (-2,0)

A:

Q: Find the 4th iteration value of an extremum (maximum/minimum value) of f(x) = 0.25sinh(2x) - bx² -…

A: The function given is as follows: fx=0.25sinh2x-bx2-cx+d Where, b=3, c=5, and d=6. Hence the…

Q: Find the (x, y) critical point (s) of the function f(x, y) = 2x³ + y² − 9x² − 4y + 12x − 2 . Then…

A:

Q: Find all the local maxima, local minima and saddle points of the function f(x,y)=3+2x+2y-2x2-2xy-y2

A:

Q: Find the critical point of the function f(x, y) = – 7 2x + 5x2 - 8y – 5y? |

A:

Q: Consider the function f(x)=x2e^4x. Determine the critical point(s) of the function and locate all…

A:

Q: Given f(x, y) = 2 – 27x – y3+3y?. Find all critical points of the following function and classify…

A:

Q: find all of the critical points and local maximums and minimums of each function. (b) f(x) = Vx – 2,

A:

Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

A:

Q: b. Find the orthogonal trajectories for the family of curves x² + y² =C².

A: we have to find the orthogonal trajectory of the given family of curve

Q: Find the critical points of the function f(x,y)= -2x^3 -4xy +2x -5y -1 and classify them as local…

A:

Q: y = 3 – 2x + x?

A: In this question, we need to find the critical points and test for maxima/minima of y=3-2x+x2.

Q: 5 Find the point X to minimize the function f(x1, x2) =1+¤1 +2x2+ from the strating point X, = using…

A: We are given the following optimization problem : f(x1 , x2) = 1 + x1 + 2x2 + 5/x1 + 10/x2 And we…

Q: a) Find the critical points of the function f(r, y) = x* + y² – 6zy + 6x + 3y Classify the critical…

A:

Q: Find the critical point(s) of the function f(x, y) = -2x3 – 4xy + 2x – 5y – 1 and classify them as…

A: We have to find the critical point(s). So, we find ∂f∂x,∂f∂y. To classify the critical point, we…

Q: Find and classify the critical points off (x) = 6x°(5 – x)° as local maxima and minima.

A: Given that f(x)=6x55-x6 First let's find the extreme points, f'c=0 Take the derivative for f,…

Q: 3. Find the critical points of the function f(x, y) = 4x2 + 9y2 + 8x-36y + 24 and use the second…

A:

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…

A:

Q: Determine all the critical points for the function y = Vx² (2t- 1)

A: Given function is in two variables x and t For critical points we calculate Partial derivatives…

Q: 2. Determine the critical points of the function: R(y) : y2 – 6y -

A:

Q: Find the critical point(s) of the function f(x, y) = -2r³ – 4ry + 2x – 5y – 1 and classify them as…

A:

Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: Find the critical numbers of the function. g(y) = y-5/y2-3y+15

A: Given function is, g(y) = y-5/y2-3y+15

Q: Determine all the critical points for the function f(t) = Vt² (2t – 1)

A: The given function is ft=t232t-1. Critical points are the points where the function is defined and…

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: Find the critical point of the function f(x, y) - 4+ 7x – 5x² + 6y + 7y?

A:

Q: y = x* – 4x +1

A:

Q: The critical point(s) of the function z= 2x²-4xy-2y²+3x-7y+6 is/are...

A: In this question, we need to find the critical points of the function z = 2x2-4xy-2y2+3x-7y+6.

Q: Find the critical point(s) of the function f(x, y) = 6x²y – 12a2 – 3y? and use the second derivative…

A:

Q: Find the critical point of the function, then determine if it is a local maximum, local minimum, or…

A:

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.