12. Let f (x) = x + find all the critical %3D points and use the second derivative test to prove if they are max or min.

Q: Find all critical points of f(x,y) = 1/x - 1/y + xy and classify each as a relative minimum,…

A: We use second order partial derivative test to find relative maximum and minimum, saddle point

Q: Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the…

A: Consider the given function. fx,y=2xy+y2+2x-1 Find the derivative with respect to x. fx=2y+2 Put the…

Q: Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the…

A: To find critical point in which given function has relative maximum and minimum.Where…

Q: 11. Use the Mean Value theorem to show that f(x) = 2x sinh (æ – 1) + 2" – x has a critical number…

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Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

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Q: Suppose that the FIRST DERIVATIVE of a function f is given by f' (x) = (x – 3)² (z² + 5x). Find the…

A: We find the critical numbers by solving f'(x)=0

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

A:

Q: 2. Find the local maximum and minimum values and saddle points (if any) of the function f(x, y) = xy…

A: Here, the given function is: f(x,y)=xy-2x-2y-x2-y2

Q: Suppose (1, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: As we know from the double differentiability test, When rt-s2>0 and r>0 then minima will…

Q: Use the second derivative test to identify any critical points and determine whether each critical…

A: Second derivative test : Suppose (a,b) is a critical point of f. Assume fxx,fyy,fxy are defined and…

Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* -x has a critical number…

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Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to…

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Q: 5. Use the given derivative to find all critical points of f and at each critical point determine…

A: Given that, f'(x)=4x3-9x

Q: Find the global maximum and minimum of the function on the given…

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Q: Suppose (2, -1) is a critical point of a function f with the continuous second derivatives. If fxx…

A: We need to choose correct option.

Q: Find the maximum or local minimum f(x)=sinx.[0,4]

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Q: 9. Find the local minimum and local maximum values using both the First and Second Derivative…

A: To find the local minimum and local maximum values.

Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x - 1) + 2* – x has a critical number…

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x – 1) + 2" – x has a critical number…

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Q: b) The critical points for the function f(x, y) = x³ + xy² + 6x² + y² are (-1,3), (–1, –3), (-4, 0)…

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Q: Use the first derivative test to find the critical points, local max and local min points (need y…

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Q: Consider the function ƒ(x) = x3. Where is the critical pointof ƒ? Does ƒ have a local maximum or…

A: Given  ƒ(x) = x3

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

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Q: Why does the maximum and minimum points for y = f (x) occur among the minimum and maximum points for…

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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: (5) Use the first derivative test to classify the critical numbers of the function s(r) = 2¹-4r³+17.…

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Q: Find the minimum and maximum values of f(x) = on the interval [6,7] by comparing values at the…

A: We will see that function retains its sign in the given interval and in decreasing function. hence…

Q: Suppose (0, 2) is a critical point of a function with continuous second derivatives. In each case,…

A: The discriminant of a function, f at x,y is calculated using the formula: D=fxxfyy-fxy2 . If…

Q: 4. Find and classify the critical points of the given function by using Second Derivatives Test. 1 1…

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Q: Compute the derivative of g(x) = | 1 dt. 2 1+t5 2" 1+æ15 1+25z 2" In 2 1+æ15 1+25z 2" 1+a15 1+25z 2"…

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Q: Q2: Find all critical numbers of the function f(x) = (x- 2)2/3 +1 and classify each critical point…

A: Here we will find out the required value.

Q: 12 11. Find the critical points of f(x) 4x? ). Then use the Second Derivative Test to determine if…

A: Here, we need to find the critical points of f(x)=x127x3-4x2. Now, f'(x)=6x2x-10xx and…

Q: Find the critical points of f(x, y) = x³ – 6xy + y³. Use the second derivative test to classify each…

A: For the solution follow the next steps.

Q: Find the critical points and the intervals on which the function f(x) = (x³ - x) e* + 4 is…

A: To find out critical values, take derivative, apply product rule

Q: 5. Use the concept of limits to find derivative of f(z) = (2z + 1)3 at z = -i.

A: Given function is f(z)=2z+13 We have to find the derivative of the given function at z=-i.

Q: Find the critical points of the function f(x, y) = y² + x?y+x² – 2y and use Second Derivative Test…

A: Follow the steps below to yield the result . Calculate . Find the critical point by solving the…

Q: On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

A: The given function is fx=sinx Differentiating w.r.t. x to both sides- f'x=cosx To find the critical…

Q: Consider f(x) = xlnx on the interval [1,6]. When will the first derivative equal zero? For each…

A: Given that: f(x) = xlnx   x∈[1,6] To find: When will the first derivative  equal to zero. And for…

Q: ) Use the second derivative test to classify each critical point of f (x,y)=-x' +4xy- 2y² +1 as a…

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Q: Suppose the derivative of a function is x2 + 2x -3. a) On which open interval/s is the function…

A: Consider the given: Given:f'x=x2+2x-3 Find the critical numbers: Substitute…

Q: Suppose (1,1) is a critical point of a function f with continuous second derivatives. In each case,…

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Q: 3. Find the critical points of the function f(x,y)=xln(x+y) Use the Second Derivative Test to…

A: The given problem is to find the critical points of the given function and use second derivative…

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of…

A: Given: fx=x3+ax2+bx fx has a local minimum at x=4 . fx has a point inflection at x=1 . Since fx…

Q: Determine the local extrema for t(x) = -3x3 - N2 - 90x +1 using the First Derivative Test. %3D

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Q: Compute the derivative of g(x) .3 = [ 1 dt- 1+ t5 3x2 1+ x15 1+ 25x 3x2 2" In 2 1+ x15 1+ 25a 23 1+…

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Q: Use the second derivative test to identify any critical points and determine whether each critical…

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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 points/max/mins: Of the curve: y=2xln(x)-x2

A: I am attaching image so that you understand each and every step.

Q: The stock price for a certain corporation can be approximated for the years 2012 through 2017 by…

A: Given that                                                         f(x)=6.3x2-168x+1199 derivative…