Find the linearization of the function z = x(sqrt(y)) at the point (-5, 49).

Q: Find the derivative of the function. 4x² +9 %3D y'

A: Differentiate w.r.t to x

Q: Apply derivative to determine the vertex of the parabola y = x² + 2x + 2.

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Q: Determine the slope of the curve y =1/x+1 at point (−2,−1).

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Q: Find the equation for the curve in the xy-plane that passes through the point (1, -1) if its slope…

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Q: Find the derivative of the function. x² + 2 y = 2 – , - 2 -&x(x² + 2, y' = (2² – 2)4

A: Given: The function is, y=x2+2x2-27. The objective is to find the derivative of the function.

Q: f(x) = v3x – 5 %3!

A:

Q: Find the points of intersection of the line y = 5 x with the curve y = 3 x + x^2

A: In order to find the point of intersection of given line line and curve , we must find values where…

Q: Use the Chain Rule to find the derivative of the function. y = (2x² - 9)3

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Q: Classify the stationary points of

A: For part (3) We have to classify the stationary points of the given function. For part (a) The given…

Q: An Object moved in horizontal coordinate line according to f(x) = x^3 - 6x^2 , where f is directed…

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Q: Find the gradient of 3e In(4x - 3) when x = 1.

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Q: Determine and distinguish the stationary values of the function f(x, y} = x² – 6x² – 8y². -

A: We need to find the stationary value of f(x,y)=x3-6x2-8y2   For that first we need to find the value…

Q: Find the direction in which the function is increasing most rapidly at the point Po. f(x.y) = xy? -…

A: Given,     f(x,y)=xy2-yx2

Q: Find the slope of the line normal to the curve y = x³ - 2x +1 at x = 2 -

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Q: Find the X coordinates to the curve Y= X^5 - 5X^4 when the gradient = 0

A: Given equation is Y= x5- 5x4 Gradient =0

Q: Find the slope of the curve 1 at the point P (2, ;).

A: Explanation of the answer is as follows

Q: estimate using the Linear Approximation and find the error using a calculator. 9^1/3 − 2

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Q: Use the Chain Rule to find the derivative of the function. y = (2x2 − 3)3 y' =

A: The chain rule to find the derivation is,

Q: Find the point on the curve y = sqrt x that is closest to thepoint (3,0)

A: Given curve y=x Let A(x,y)  be a point on the curve and let B(3, 0) So distance between A and B is…

Q: Find the orthogonal trajectories for the family of curves y=c1x4

A: First of all rearrange the given equation in such a way that both the variables be on one side of…

Q: Find the equation of the lines tangent to the curve x2 + y2 = 4 and parallel to the y-axis ?

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Q: /hat is the maximum slope of f(x,y,z)%3DyeX-x2sin(z) at the point (0,7,5)? ound to the nearest…

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Q: Find the curve in the xy-plane that passes through the point (9,4) and whose slope at each point is…

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Q: Use the deffinition of derivatives to deffrintiate y= -x3+3x-6

A: Here the given function is

Q: Plot the function fx) = x3- 2x2-10sin?x-e0.9x and its derivative for %3D -25x54 in one figure. Plot…

A: The given function is  f(x)=x3-2x2-10sin2(x)-e0.9x and so the differential of the function is ,…

Q: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given, the curve y = ƒ(x) in the xy-plane that passes through thepoint (9, 4) and whose slope at…

Q: Find the coordinates of the point/s on the curve y = 2x2 which are closest to the point ( 9, 0 ).

A:

Q: Find the slope of the curve y=x4 at x=3.

A: Find the slope of the curve y=x4  at    x=3.

Q: Use calculus to find the point on the curve y = 3x−1 that is closest to the point (2, 0).

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Q: what is the gradient of f(x)=3x2-2x at x=-2?

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Q: Use the linear approximation to estimate

A: In this question, by using a linear approximation to evaluate the value of the expression using…

Q: Consider the linear function y = ax + b. If x changes at a constant rate, does y change at a…

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Q: Find the points on the curve y = 2x3 - 3x2 - 12x + 20 where the tangent line is a. perpendicular to…

A: Find the slope of the line y= 1- (x/24)

Q: Use the Chain Rule to find the derivative of the function. y (4x2 - 7)3 %3D

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Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

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Q: The slope of the curve y^2-xy-3x=1 at the point (0,-1)

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Q: Find the slope of * y+ Vx+ y =x at (3,1)

A: A detailed solution is given below

Q: Find the gradient of the curve y = x° – x2 – 8x – 2 at the point on - - - the curve whose…

A: As we know that; The expression for the gradient or slope; m=dydx And The Power law; ddxxn=nxn-1

Q: Find the gradient of the curve . Y=4x^2 at x=3

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Q: y = Vz3 -4z-2 %3D

A: Given: y = z3 - 4z - 23   To find the derivatives.

Q: Find the slope for f(x,y) = xeyat P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: We have to find slope

Q: Find the x-coordinates of all points on the curve y = 12x" - 96x° - 168x + 26x + 91 where the…

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Q: Find the equation of the line tangent to the curve y = 4x² – 8x + 4 at the point(5, 64). -

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at…

Q: 2а3x at (a, a) ,2 x2+a²

A: Given curve is,

Q: Find the derivative: y = (3x² – 2x) Væ5 – 2x + 2 %3D

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Q: Differentiate the function y=(1−x)3 without using the chain rule.

A: Differentiation: y=(1-x)3 y=1-3x+3x2+x3ddx(xn)=nxn-1

Q: Find a formula for the linear function whose graph is a plane passing through the point (4, 3, -2)…

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