1. Solve the following below A) Use the second derivative test to find all the local...

1. Solve the following below

A) Use the second derivative test to find all the local maxima, local minima and saddle points of f(x,y)=x^2 +xy+y^2 +y

B) Find the absolute minimum and maximum values of f (x, y) = x^2 + y^2 − 2x on the closed triangular region with vertices (2, 0), (0, 2) and (0, −2). [First find interior critical points, then critical points on the boundary, i.e. on each edge of the triangle. Finally, include the vertices of the triangle in the list of candidates.

Expert Solution

milcah answered 2 years ago

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable....

Find the relative extrema, if any, of the function. Use the second derivative test, if applicable. (If an answer does not exist, enter DNE.) g(x)=x^3-6x relative maximum (x, y) = ( , ) relative minimum (x, y) = ( , )

Find maximum, minimum and saddle point by using the second derivative test: Show all the work...

Find maximum, minimum and saddle point by using the second derivative test: Show all the work f(x, y) =8xy-x^4-y^4

Use the First Derivative Test to find the exact location of all the relative extrema of...

Use the First Derivative Test to find the exact location of all the relative extrema of the given function. 1. f(t) = t^3-3t^2, Domain [-1, +infinity) 2. f(x) = 3x^4-2x^3, Domain [1, +infinity) 3. f(x) = (x+1)^2/5. Domain [-2,0) 4. f(x) = √ x(x-1), Domain [0, infinity)

Use the first derivative test to determine the location of each local extremum and the value...

Use the first derivative test to determine the location of each local extremum and the value of the function at this extremum. f(x)=4xe-4x 1. The function has a local maximum of __at x=___.

Use the First Derivative Test to find the relative extrema of the function, if they exist....

Use the First Derivative Test to find the relative extrema of the function, if they exist. 16. f(x) = x^4 - 18x^2 + 8

Find the derivative of the function below.

Find the derivative of the function below. Find the derivative of the function below.

Find the local maximum and minimum values of f using the First Derivative Test. f(x) =...

Find the local maximum and minimum values of f using the First Derivative Test. f(x) = x2 x − 2 local maximum value local minimum value

For the given function use either the 1st or 2nd derivative test to calculate the following: (Show all...

For the given function use either the 1st or 2nd derivative test to calculate the following: (Show all work!!) (must show test used) a). all critical points b). draw the sign diagram c). find all relative extreme points. d). list the intervals where the function increases and decreases. e). all inflection points f). intervals of concavity g). sketch the graph

Use the Second Derivative Test to locate any relative extrema, if they exist. (Round your answers...

Use the Second Derivative Test to locate any relative extrema, if they exist. (Round your answers to two decimal places. If an answer does not exist, enter DNE.) f(x) = 1 3 x3 + 5 2 x2 + 6x − 5 relative maximum (x, y) = relative minimum (x, y) = Here is a screenshot of the problem: https://gyazo.com/7c25d969fc2d85eeee2bbafe0cec23a3

Use the given function, its first derivative, and its second derivative to answer the following: f(x)=(1/3)x^3...

Use the given function, its first derivative, and its second derivative to answer the following: f(x)=(1/3)x^3 - (1/2)x^2 - 6x + 5 f'(x)= x^2 - x - 6 = (x+2)(x-3) f''(x)= 2x - 1 a) What are the intervals of increase and the intervals of decrease b) Identify local min and max points c) What are the intervals where the function is concave up, concave down and identify the inflection points

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