(a) Find the gradient of the curve at the point Q. (b) Given that the product of gradients of tangent and normal is -1, derive the equation of the normal to the curve at the point Q. I

Q: a. Determine the equation of the tangent line to f(x) = 2-x² 1 + x b. Determine the equation of the…

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Q: 5.Find the equation of tangent and equation of normal to the curve, 1 -3xy 5-8y' at the point (1.1).…

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Q: 5. Find the gradient of the curve i) y = 3e-2x – 1 at the point where x =. ii) y = xv2x - 3 at the…

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Q: Find the gradient of the curve and the equation of the tangent line at the specified point x*y' -…

A: Given: Curve, x2y3-2xy=6x+y+1; and point 0,-1

Q: 5.Find the equation of tangent and equation of normal to the curve, 1 (3x - 1) 3xy = 5-8y' at the…

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Q: Find equations of the tangent line and normal line to the given curve at the specified point in…

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Q: xyz), find: (1) the gradient of fat (1.1.2); (2) the directional derivative

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Q: Find the equation of the tangent line to the curve at (2, 1): x^2 + 4xy + y^2 = 13

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Q: Find the slope of the tangent line to the curve (2x + 4y+ /2xy = V16 + V12 at the point (6, 1). %3D…

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Q: II. Find the equation of the tangent and normal to the curve at the indicated point 1. y =x at (2,4)

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Q: a) Determine the equation of the tangent plane of the graph of the function f(x, y) = 3x²y - 2y³ In…

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Q: Find the gradient of /x, y. 2) eand the largest value of the directional derivative of fox. y. zi…

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Q: Find the equations of the tangent and the normal at the point indicated.   a2y = x3 at (a, a).

A: To find the equation of tangent and normal at the given point.

Q: Determine the point on the curve of y=4/x where the gradient of the tangent to the curve is -1

A: To determine: The point on the curve of at which gradient of tangent to the curve is . Given: The…

Q: The Normal to the curve 2x² – y² = 1 at the point (1,1)

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Q: Find the tangent and normal to the curve y=2e-x/3 at the point where the curve meets the y-axis

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Q: Find the gradient of y = e" at the point (1, e).

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Q: x = e' and y = te %3D

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Q: Find the equation of the tangent and normal to the curve y = x + x at(0,0).

A: We have to find the equation of tangent and normal for the curve: y=x+x23 at the point 0, 0 We know…

Q: 6. Find the equation of the tangent line to the curve r* - a*y" = 12 at the point (-2, 1).

A: the equation of the tangent ( x0, y0 ) to the curve y=f(x) is    y – y0 = f ′(x0)(x – x0)

Q: Find all points​ (x,y) on the graph of y=x/(x−1) with tangent lines perpendicular to the line y=x−8.

A: The given function for the tangent is, Differentiate the above expression to get the slope of the…

Q: IL. Find the equations of the tangent and normal lines at the paint indicated. b. 4x - 4y - sin(x +…

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Q: Find an equation of the tangent plane at the given point. f (x, y) = x/√y,  (4, 4)

A: Given : The function is f ( x, y) = xy and point ( 4, 4 ).

Q: Find the equation of the tangent and normal line at the point indicated. Sketch the curve. у %3 х3 —…

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Q: Find an equation of the tangent line and normal line to the curve at the given point for the…

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Q: b) Find the gradient of the tangent to the curve y= at the point with x=1.

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Q: For the function f(x, y) - y? find a unit tangent vector to the level curve at the point 3 (- 4, 5)…

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

Q: Find the gradient of the tangent line to y when x =- 1

A: The explanation of answer as follows

Q: Find the gradient of the curve and the equation of the tangent line at the specified point x*у' -…

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Q: For the function f(x) = x² – 4 at the point (4, 12), find: a. the slope of the curve using the…

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Q: f(x,y) = 4x² + y² + 2 at the point wherex = 1 and y = 1.

A: The equation of the tangent at point (1,1) is: z=f(1,1)+fx(1,1)(x-1)+fy(1,1)(y-1)

Q: Find the slope of the curve and equations of the tangent and normal to the curve at the given point.…

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Q: Question 10. Find the gradient of the curve f(2) = -2³ + 10z? – 3 at z = 4. Gradient =

A: Let's find.

Q: Find the equation of the tangent plane to the graph of the curve f(x, y) = x² + y² at the point…

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Q: Find the equation of the tangent line and the normal line of the curves at given point 1. y = x V16…

A: Equation of tangent line Consider y=x16+x2slope of the tangent line is dydx  at…

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 equations of the tangent and the normal at the point (2,2) at x² – 2xy + y² +2x + y - 6 = 0

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Q: a) Find the equation of the tangent line to ƒ at (3, –27/17). y = -16.816x+48.198 b) Find the…

A: We find dy/dx using the quotient rule then we plug x=3 in it

Q: 10. Use differentiation to find the gradient of the curve y = ax sin(bx) at x = 3. 7. -17 b= 19

A: Please refer to the image below

Q: The gradient of the tangent to the curve y = 2e"- 3e" at the point where x=0 is %3D A 5. B 7. C -L D…

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Q: Determine the gradient and equation of the tangent to the curve f(x, y) = 0 in the point or (a)…

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Q: Find the equation of the tangent line and normal line to the following curves at the indicated…

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Q: 5. What is the slope of the tangent line to the curvex²e-2x - y = 0 at the point (-1, e2²)?a. a. 4…

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Q: find the equation of the tangent line to the curve at the point corresponding 4o the given value of…

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

Q: The gradient of the tangent to the curve = 4x + y at the point (0, 1) is D - 2

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Q: Find the equation of the normal to the tangent line for the equation x'y+ xy² +x² + y² = 0 at the…

A: Note that, according to Bartleby guidelines, we can answer only the first question in the case of…

Q: Find the equation of the tangent line at (2,2) on the curve x² + xy + y² = 3

A: Topic = Derivative

Q: Find the values of x for which the gradient of the tangent to the graph of y=f(x) is equal to the…

A: We have to find the values of x for which the gradient of the tangent to the graph of y=f(x) is…

Q: Find the gradient for the curve defined by y + xy = 3 at the point (1,2)

A: Gradient to given curve

Q: The gradient of the tangent to the curve (image attached)   at  x = 2  is  4. The value of  a  is…

A: The gradient or the slope of the tangent to the curve: y=fx at x=a is f'a.  It is known that…