What is the range of the function y = cos™+(x +1)? 0(-2,0] o [0, r] T O (0, T)

Q: 9. State the Second Derivative Test for functions of two variables z = f(x, y)

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Q: What does it mean for a function of two variables, f (x, y),to be differentiable at a point (a, b)?

A: A function differentiable at a point has a derivative that is defined at that point. This is defined…

Q: What are all absolute and relative extreme values of the function f(x)=– sin z on the interval (0,…

A: Given function f(x) - f(x) = -sinxDifferentiating on both sides with respect to x - f'(x) =…

Q: Find the derivative of f : R³ → R² defined by f(x, y, z) = (-3x²y, e-3y-2:). The derivative f' : IR³…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the maximum rate of change of f(x,y)= e^x^2 at (3,0) and the direction in which it occurs.

A: GIVEN DATA : Function fx,y=ex2        TO FIND : Maximum rate of change at 3,0 and the direction  The…

Q: Find the maximum rate of change of fat the given point and the direction in which it occurs. f(x, y)…

A: Note: where △f(x,y) = ∂f∂x,∂f∂y

Q: Bounded by the curve y = (x + 3)², the x axis, and the lines x =-3 and x= 0. %3D

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Q: 4xy* :- find f,,f, at point (4,1) for f(x,y) = x’e**Y

A: I have used partial differentiation

Q: Illustrate local linearity for the function f (x) = xsinx at x = l.

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Q: 3. (D - 3D? + 4)y = 40cos2x + 6

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Q: (b) Apply the First Derivative Test to identify the relative extrema. (x, y) = ( ,1 2 relative…

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Q: One of the critical points of the function z = f(x,y) = 4x -12xy+ y +1 is (0,0,1). [Notice that I !!…

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Q: Fexsys = -xy + %3D 2 what are Hhe two criticas ints?

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Q: What is the formula for the linearization of a function f at the point x = a? %3D

A: Given :To provide the formula for linearization of a function f at the point x=a

Q: Autocorrelation function is maximum at the origin, i.e., |Rxx (7) |S Rxx (0) XX

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Q: Find the derivative of the function = V(=² – 3)* 6, f(x) at x = 2. %3D f'(2) =

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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: What is the maximum slope of f(x,y,z)=yex-x2sin(z) at the point (0,7,5)?

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Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. Зx +…

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Q: What is the maximum slope of f(x,y,z)=ye^x-x^2sin(z) at the point (0,7,-3)?

A: Given the function fx,y,z=yex-x2sinz and the point 0,7,-3. Computing the partial derivatives,…

Q: Why is the function f(x)= cotx not differentiable on the interval [0, pi] ?

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Q: Given the function f(x) = (x-2)2 + (y-3)2 (i) Find the critical points. (ii) Using the second…

A: The given function is: f(x,y)=(x-2)2+(y-3)2

Q: Find the relative extrema of f (x) = 7+ 144x – 9x? using both first %3D and second derivative tests.…

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Q: How can linear approximation be used to approximate the changein y = f(x) given a change in x?

A: Given;                 y=fx How can linear approximation be used to approximate the changein y=f(x)…

Q: Find the derivative of the function f(x,y,z) = x² + 2y? – 3z2 at the point v =. Po = (1,1,1) in the…

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Q: The partial derivative of function respect to y* f(x, y) = x² + y/y? %3D

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Q: Where is the function defined by f(x) = In (x) increasing? Where is f(x) decreasing? Where is the…

A: Given a function: f(x)= ln(x) and the function is defined in the domain x∈(0, ∞)Then, f'(x)=1x

Q: F(1), p(y) - y - 1, F(Y) - F(y - 1), y - 2, 3, ...

A: Suppose that Y is random variable that takes on only integer value 1,2,.. and has distribution…

Q: How is the antiderivative of a function related to the function?

A: Given: antiderivative of a function related to the function.

Q: Find the maximum rate of change of fat the given point and the direction in which it occurs. f(x, у)…

A: Given function and point is

Q: Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and…

A: Given function is

Q: The directional derivative of f(x, y) (3, 4) is -In(x² + y²) at the point P(1, 5) in the direction v…

A: Definition used -          Directional derivative at the point -     The rate of change of f(x, y)…

Q: The derivative of the function Ve-tanh a is O y = -sech3x vetanh z 2 O y = -sech?x Ve-tanh / 2 O y =…

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Q: The maximum rate of change at a point on a function f(x,y,z) is да ylgr

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Q: Find local extrema  f(x,y)=-x^2-y^2-5x-7

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Q: Find the critical points for the function f(x, y) = x² + y³ + 2xy – 2x – 7y. (You do not need to…

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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: The general solution of Besseal function is given by y = c,J,(x) +y,(x)

A: Given statement, The general solution of Bessel function is given by y=C1Inx+ynx

Q: find the equation of tangent line of function f(x)=csc(x)-cos(x)1/2 at the point ((2*3.14)/3,…

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Q: What function should be used to minimize the distance between y = x + 5 and the point (3, 1)? O D(æ)…

A: Explanation of the solution is given below...

Q: Find a simple closed curve C with counterclockwise orien- tation that maximizes the value of f t* dx…

A: Given an integral. We need to find the C that maximises the value of the integration.  Let's start.

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: We have to solve

Q: Find the direction of the maximum rate of increase of f(x,y, z) = y²sinxz² at the point (0,3, –1).…

A: Given the function f(x,y,z)=y2sin(xz2) And the point (0,3,-1)

Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, Y)…

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Q: What is the derivative of f(z) = (z³ –- (z – 1)º)*? %3D

A: Given function is f(x) = (x3 - (x-1)3)3

Q: 12. Differentiate the function (use chain rule): y = 2x2 Vx+1'

A: To differentiate the given function

Q: Use the Second Derivative Test to determine the relative extremum trema) and saddle point(s), if…

A: This is a problem related to maxima and minima of the function. By first derivative test we will…