Find the critical points of the function f(x,y) = x^4 + y^4 - 196xy and use the Second Derivative Test to classify each critical point.

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = Sin2x ; 0<x<n

A: i) The given function is fx=sin2x. Given that the domain of the function is 0,π. Obtain the first…

Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

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Q: Find the critical points of f(x) and use the Second Derivative Test (if possible) to determine…

A: Given that the function is        f(x) = x e-x^2

Q: According to the criterion of the first derivative, the image function has a point: f(x) = x2 + 10x…

A: The given function f(x)=x2+10x+21

Q: find the critical points and apply the Second Derivative Test (or state that it fails). f (x) = sin2…

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Q: Find the Equation of tangent line of the function f(x)=1+csc(x)-√cos(x) at the point…

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Q: 2. Find the third order derivative of y = In(secx + tan x). a. secx b. secx tan x c. - sec(x) + 2…

A: Explanation of the answer is as follows

Q: IT ) Verify that ,0) is a critical point of f(x, y) = y² - 2y cos x. Then use the second derivative…

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Q: Find the critical points, use the second derivative test, and determine the relative maximum and…

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Q: Explain how the First Derivative Test determines whetherƒ(x) = x2 has a local maximum or local…

A: Given:   f(x) = x2 To determine whether f(x) has a local maximum or local minimum at the critical…

Q: find all relative extrema of thefunction. Use the Second Derivative Test whereapplicable. f(x)=6…

A: Given:            fx=6x-x2 Second derivative test definition: Suppose that x = c is a critical point…

Q: Sketch the x^2 And the derivative And integration

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Q: Find the relative extrema of f(x) = 8+ 126x – 7x2 using both first and second derivative tests. f…

A: If second derivative is less than zero then there is relative maxima.

Q: Locate the critical points and identify which critical points are stationary points. f(x) = |sinx|

A: Given:

Q: Use second derivative test, If f(x) = 25x + 10 then f(x) has a 3 local maximum at the point_

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Q: 3. Why first derivative is zero at local maximum and local minimum of function in an open interval?

A: Given, Why the first derivative is zero at the local maximum and a local minimum of function in an…

Q: second derivative

A: To find the critical point(s) of the function f(x, y) = xy + ln x + 2y^2  Then by  use the second…

Q: By using the second derivative test for functions of two variables, find three positive numbers…

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Q: Find all of the critical points of the function f(x, y) = x²y². Can the second derivatives test be…

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Q: Find all relative extrema of the function f(x) = x* – 4r +2 by using | the Second Derivative Test…

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Q: Find the critical points/number of the function h(x) = e^x sinx-sinx+cosx by applying derivatives.

A: First calculate its derivate then equate it equal to 0 to obtain the critical points. h(x)=exsin…

Q: The function has only one critical point at x = VIn(a). Use the Second Derivative test to identify…

A: Solve g'(x)=0 to obtain the critical points. Then evaluate g'' at those critical points. If it is…

Q: The second derivative test fails when f" is zero or does not exist at the critical number of the…

A: Given data: The value of the second derivative of the function is f''=0.  Suppose at the given point…

Q: The total derivative of f(x,y) = ylnx  is

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Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: Are critical numbers from the first derivative used in the test for concavity?

A: We have to tell that  critical numbers from the first derivative used in the test for concavity or…

Q: What are the critical points of sin(x2-1), at the closed interval [-1,1]?

A: Given: The critical point is a funtion is the point where the derivative of the funtion is zero.…

Q: A metal storage tank with fixed volume V0 = 360π m^3 is to be constructed in the shape of a right…

A: To find: The dimensions will require the least amount of metal. Given information: A metal storage…

Q: Find the relative extrema using first derivative test   f(x)=(x-2)^6

A: Consider the function f(x)=(x-2)^6

Q: Find the x-value for all relative extrema of f(x) using the first derivative test. Specify whether…

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Q: given the function f(x) = (x+4)^2 + (y-2)^2 (i)find the critical points (ii)using the second…

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Q: 4. Given is the equation y = a) the critical points, b) classify the maximum and minimum point using…

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Q: Determine the Derivative of the Function: 1. y = ex - 1/ex + 1 2. y = x22x 3. y = 43x^2 4. f(x)…

A: Find derivatives

Q: 2. Use an example to show how to use the First Derivative Test for critical points

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Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. f(x) =…

A: As per the question, we need to find out the x value of the extreme, for bubble 3 only. For (3),…

Q: Calculate first, second, and third derivative values for function, f(x) = -x2 + 5x + 3 at points x =…

A: Forward difference Consider a linear interpolation between the current data value (t0,I0) and the…

Q: Find the critical point of the function. Then use the Second Derivative Test to determine whether it…

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Q: What

A: The correct option is (B).

Q: Find the critical points of f(x) and use the Second Derivative Test (if possible) to determine…

A: At critical points the first derivative of the function will be zero , Second derivative test At…

Q: How do you find the partial derivative of a given function using the definition formula?

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Q: 2. Find the critical points of f(x, y) = x³ + 2y³ – xy and analyze them using the Second Derivative…

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Q: Find the general anti-derivative of f(x) = 3. + Vx on a continuous interval. Please select file(s)…

A: topic - integration

Q: Use implicit differentiation to calculate the value of derivative y' at the solution point (2, y) =…

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Q: Find the derivative car (x+y) = yrinx

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Q: Find the critical numbers of the function and apply the First Derivative Test to identify all…

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Q: Find all critical numbers and use the Second Derivative Test to determine all local extrema.

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