Find a point P(x, y) on the graph of the function f (x) = 3x² + 2x + 1, where the normal line to this function at the point P (x, y),contains another point (9,5).

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

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Q: Find the gradient of the function at the given point. In(x2 - Y) - 9, (3, 8) Vz(3, 8) =

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Q: Find the equation of the normal line (NL) to the graph f(x)=x³ – 4x atx = 3 .

A: We need to find derivative.

Q: Find the normal lines to the curve xy + 2x - y = 0 that are parallel to the line 2x + y = 0.

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Q: i) Find the critical numbers of function f (x) = x/x+3 TV. ii) If 2x- y=k is the equation of a…

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Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ + 10

A: Here we have to find the orthogonal trajectories

Q: Find the gradient of the function at the given point. In(x2 - y) - 6, (2, 3) Z = Vz(2, 3) = %3!

A: To find out the gradient of the function at the given point..

Q: Find the normal lies to the curve ru + 2x – u = 0

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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: Find the equation of the normal line of y = 8 – x³ at (-1 , -3) а. 8-Зу — х %3D 0 b. х— Зу — 8 %3D 0…

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

Q: Find the gradient of the function at the given point. In(x² – y) – 8, (3, 8) Vz(3, 8) =

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Q: What is the equation of the normal line to the curve x2 + y² –6x- 2y=0 at (2,4)? A x+3y+10= 0 B…

A: The given curve is x2+y2-6x-2y=0...(1) To find the equation of the normal line to the given curve at…

Q: Find the equation of the normal line in the curve x2 − 6x + 2y − 8 = 0 at x = 3

A: We need to find equation of normal line.

Q: Find the two points on the curve (xy)² = 2 – xy where the slope of the normal line is I.

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Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

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Q: What is the equation of the normal line to the curve x2 + y2 - 6x-2y=D0 at (2,4)? none of the given…

A: Given curve is: x2+y2-6x-2y=0To find equation of normal to curve at (2,4), we need slope of line at…

Q: Find the gradient of a normal line to the parabola y=x^2+5x-9 at the point (1,1)

A: In this question, the concept of slope is applied. Slope A line's slope or gradient is a number that…

Q: Find the linearization of the function z = x/j at the point (3, 64). L(x,y)

A: According to the Bartleby guideline only one question can be solved at one time, post the remaining…

Q: Find the equation of the normal line to the graph y= x In x that is perpendicular to the line x - y…

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Q: 10, 6J. the Midpoint Rule with timate the folllowing. IL x. v) da How could you improve your…

A: As m=n=2 Therefore let us take the subintervals as: 0,3 and 3, 6 The midpoints od these subintervals…

Q: 4. At what point on the curve x = y² – y will the normal line cross the y-axis at y = 8?

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Q: Use the linearization L(3,-2) (x, y) of f(x, y) = -x²y-xy² near the point (3, -2) to approximate the…

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Q: The equation of the normal line to the curve y = -Væ that is parallel to -6x +y = 1 (A) y + 3 = –6(x…

A: Solve by equation of normal Line

Q: Find the equation of the normal line to the curve y = 2x - x at (2, 0). O a. 2x - y = 4 O b.x - 2y =…

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Q: 4. Find the orthogonal trajectories of the family of curves y = Ce* +10

A: Given that : y = Ce2x + 10

Q: 4. Find the orthogonal trajectories of the family of curves: y = ke* %3D

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Q: Find the equation of the tangent plane and normal line to the function f(x,y)= \x +y at the point…

A: Please see the explanation below

Q: Find the equation of the normal line to the curve y = x³+ 3. at (1, 4). %3D O a. x = 1 O b.y = 4 O…

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Q: Find the average vale ot f(x)=Dx²e-2x overthe interval [-1,1]

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Q: Find the equation of the normal line to the indicated curve at the given point. 2 y = 4x+8 at Select…

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Q: Find the gradient of the function at the given point. In(x - y)- 4, (3, 8) Z = Vz(3, 8) =

A: The objective is to find the gradient function at the given point.

Q: Determine the equation of the tangent line to the graph of the function f(x)=x* – 4x atx = 3 . Also,…

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Q: Find the gradient of the function at the given point. In(x²-y)-3, (3,8) X Vz(3, 8) = z =

A: The given function,   z=lnx2-yx-3, at the point 3,8

Q: For the function h (1) = - 3z+2x-1, determine the equation of the normal line at z = 2. I' - USE THE…

A: Given: h(x)=x3-3x2+2x-1 The objective is to find the equation of normal line at x=2. It is known…

Q: Find the equation of the normal line to the curve y = x3+ at (1, 4). O a. y = 4 O b.y = -4 OC.x = -1…

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Q: The equation of the normal line to the curve x^2 + y^2 - 6x + 10y + 29 = 0 at (2, -3) is 2x + y = c.…

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Q: By utilizing Gradient Descent where initial x1=x2=Dx3%3D0, What is the approximated min. point of…

A: To find - By utilizing Gradient Descent where initial x1 = x2 = x3 = 0, What is the approximated…

Q: What is the equation of the normal line to the curve x2 + y² – 6x – 2y=D0 at (2,4)? A 3x-y+10=0 B…

A: We need to find the normal line to the curve: x2+y2-6x-2y=0 at (2,4) This can be done as follows:

Q: 4. Find the orthogonal trajectories of the family of curves y= Ce“ +10

A: Given that, Family of curves is following, y = Ce2x + 10…

Q: What is the equation of the normal line to the curve x2 + y² - 6x - 2y=0 at (2,4)? A x+3y- 10 = 0…

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Q: Find the gradient of the function at the given point. In(x²-y)-3, (3,8) X Vz(3, 8) = Z

A: for finding gradient we have to find the derivative with respect to x and y   z  = ln(x2 -y)/x - 3…

Q: Find the gradient of the function at the given point. In(x2 – y) - 3, (3, 8) Z = | Vz(3, 8) =

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Q: What is the equation of the normal line to the curve x2 + y2 – 6x – 2y=0 at (2,4)? (А) х+3у-10%3D0…

A: Please refer the attached image for complete solution. THANK YOU.

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 gradient of the function at the given point. In(x² - y) - 9, (2, 3) = Z Vz(2, 3) =

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Q: What is the equation of the normal line to the curve x² + y² -6x- 2y=0 at (2,4)? A none of the given…

A: The given curve is x2+y2-6x-2y=0 at 2,4. We know the equation of the normal line is: y-y1=-1mx-x1…

Q: Show that the average rate of change of the linear function f(x) = a over any interval say [x1,x2]…

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Q: 6) Find the orthogonal trajectories for the given families of curve 3x - y = c.

A: To find orthogonal trajectory first differentiate with respect to x then remove constant then put…

Q: Find the average rate of change of the function f(x)=x2  on the interval [x, x+h]

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Q: 2. For the curve y = x3 + 2x² + 4 a.Solve the normal line at point (-2,4) b. Locate the possible…

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