Find all the extreme values and their types from the function f defined by f (x, y) = 2y ^ 3 + 2x ^ 3 - 3xy ^ 2 - 12x

Q: The absolute minimum value of the function f(x) = –3 sinx on the interval [2, 8] is

A: To find the absolute minimum value of f(x), first we have to find the derivative of f(x) i.e. f'(x).…

Q: find all critical points of the function f (x) = sin^−1 x − 2x

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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: Analyze the critical points of f (x) = (2x − x2)ex .

A: fx=2x-x2ex Differentiating with respect to x, we get…

Q: ) The tangent line to y = f(x) at (-5, 2) passes through the point (-7, -5). Compute the following.…

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Q: 4. Is the function given by G(x) 1 x-1 the interval (0, ∞)? Why or why not? continuous over

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Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1)      ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

Q: If 1– cosh x f(x) : 3+ cosh x then f'(x) =

A: The quotient rule of the differentiation uv'=u'⋅v−u⋅v'v2.

Q: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

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: Vx + 2 Determine where f(x) = is continuous. In(3x – 5)

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Q: (4-х, XS0 10) Determine if the function y(X) = 3x, is differentiable at x =0. x>0

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Q: Find all relative extrema of the function f(x) = x* – 4x2 + 2 by using the Second Derivative Test…

A: Given, The function  fx=x4-4x2+2 We have to find the all relative extrema of the function using the…

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 two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: Let X2=mY , where 'm' belongs to set of integers. And here we have taken a parabolic path .

Q: Find the area of a triangle bounded by the yy axis, the line f(x)=4−67xf(x)=4-67x, and the line…

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Q: he first derivative of y = 3x ++ 2V - a is %3D 3 10 y' 5 5z 5 3z 3 3 O y' 10 %3D 2V14 3 O y' 3. 10…

A: To find the derivative of: y=3x15-23x+35+2x34-5x23⇒y=3x15-23x+35+2x34-5x-23...(1) Note that:…

Q: Find the x-value of the extrema by using the Second Derivative Test. Justify your answer. 1 f(x) =…

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Q: 3. Is the function given by x²-4x-5 -,x< 5 f(x) =. x-5 x+1, x 2 5 continuous atx=5? Why or why not?

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Q: Find the linerization  of f(x)=x^3  near x=1 . use that linerization to approximate (1.1)^3

A: Linearization of f(x) near x=a is given by f(x)=f(a)+f'(a)[x-a] Where f'(x) is first derivative of…

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: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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

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Q: 1 F(x) = -1. tanh 3x

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Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

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Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: Determine the extreme values of the function (exact coordinate(s) f(x) = 2sinx – x on the interval x…

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Q: Use the linear approximation to estimate Af = f(3.2) – f(3) for f(x) = 1+x² * (Use decimal notation.…

A: Given: f(x)=81+x2

Q: Find the absolute extrema of the function on the closed interval. TEX y = tan 16 ), [0, 4] minimum…

A: Given that, The function is y=tanπx16 on the closed interval [0, 4]. To find absolute extrema:…

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: Fexiy)= 2+3トなら-3A Ris Rectanghe ( (ろy)と1メ,-

A: This is a problem of maxima and minima. By using first derivative test we will find out critical…

Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Find the critical numbers of the function  f(x) = 4x - tan x

A: fx=4x-tanx Differentiating with respect to x, we get f'x=41-sec2x=4-sec2x

Q: Find the exact location of all the relative and absolute extrema of the function. f(x) = 2x – 2…

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Q: Find the derivative of a composite function using the Chain Rule or General Power Rule.  1.) y=…

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Q: Find all relative extrema of the function f(x) = x² - 4x² + 2 by using the Second Derivative Test…

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Q: Find the absolute extrema for the function over the specified domain. y = x2 5 over [ – 1, 2] -

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Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = 1+8x - 3x2

A: i) The given function is fx=1+8x-3x2. Note that, the above polynomial function is real and defined…

Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: Find the point on the line y = – 4x + 2 closest to the point (8, 9). - The function giving the…

A: Given, equation of line : y = -4x +2 And  The point : (8, 9) {outside the line}

Q: The critical points for the 4 function f(x) = x + – is:

A: Given,          The function is fx=x+4x .

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

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Q: 1. Use the first derivative test to find the location of all local extrema for 3 f(x) = -x³ +x+ 18x…

A: Dear student as per our rule in one session we can only solve one question. Please post the other…

Q: The coordinates of the critical point according to the criterion of the first derivative of the…

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Q: 4. Find the maxima/minima of f(x) = x³ – x using both 1st and 2nd derivative test.

A: Consider the function: fx=13x3-x. Find maxima, minima.   Find f'x by applying axn'=anxn-1.…

Q: 1 f(x) = (x² + 3x)² at [2,3]

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