The curve x3 + y3 = 3xy was first discussed in 1638 by the French philosopher-mathematician René Descartes, who called it the folium (meaning "leaf"). Descartes's scientific colleague Gilles de Roberval called it the jasmine flower. Both men believed incorrectly that the leaf shape in the first quadrant was repeated in each quadrant, giving the appearance of petals of a flower. Find an equation of the tangent line at the point (, 2' 2 y -2 2 -2+ (Express numbers in exact form. Use symbolic notation and fractions where needed. Let y = f(x) and give the equation in terms of y and x.) equation of the tangent line:

Q: Find the equation of the tangent line to the curve at a given point  y=x3-3x+1 (3, 19)

A: Given,

Q: Find an equation of the tangent line to the curve at the given point. y = 4x – 3x, (2, –4)

A: Given, y=4x-3x2Point=2, -4

Q: Find the equation of the tangent line to the curve (y-2)² = 4x +5 at P(1,5).

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Q: Find an equation for the tangent line to the parabola y = x² at the point P(1, 1).

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Q: (a) The curve with equation y 2   = x3 +3 x 2  is called theTschirnhausen cubic. Find an equation of…

A: We find dy/dx at x=1 and y=2  So the slope of the tangent = 9/4

Q: Find the equation of the tangent to the curve y= (5 – 6x)* at the point (1,1).

A:

Q: (a) The curve with equation y 2   = x3 +3 x 2  is called theTschirnhausen cubic. Find an equation of…

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Q: Find the equation of the tangent to the curve y= 3x' – 4x² +2x–10 at the points where the curve cuts…

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Q: Find (and simplify) the equation of the tangent line to the graph of y = 24 at x = 1.

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Q: Find the equation of the tangent line to the graph of y = 2x +- at the point (1,5).

A: We have given

Q: Find the equation of the tangent line to the curve at the given point. y: (6, 1)

A: Recall: Point - slope form : y-y1= m x-x1 ; where , 'm' is the slope and x1,y1 are the given…

Q: A coordinate of the point on the curve of y=2x3−3x−6, where the tangent at the point is…

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Q: Find an equation of the tangent line to the curve at the given point.y=8x-6x^(2), P(4,-8)

A: y=8x-6x^(2), P(4,-8)Let the equation of the tangent: y=mx+cSlope of the tangent =m =  dy/dx.

Q: The curve y = x /( 1+ x2 ) is called a serpentine. Findan equation of the tangent line to this…

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Q: Find an equation of the tangent line to the curve at the point (3, 11). х — 1 y = X - + 9 ·2 y =

A: Note: As per our company guidelines we are supposed to answer the first question only. Kidnly ask…

Q: Find the points at which the graph of the equation has a vertical or horizontal tangent line.…

A: Given equation of a graph is 4x2+y2-8x+4y+4=0 Since we need to find the points where the tangent to…

Q: Find an equation of the tangent Iine to the ollowing curve at the point (0, 5). xe' + ye* = 5

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Q: Find the coordinates of the points on the curve y= x' + 5x + 3 at which the tangent: makes an angle…

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Q: Find the​ x-coordinates of all points on the curve y = (-x^2+4x−3)^3 with a horizontal tangent…

A: We know the slope of the tangent where it is horizontal is 0. we will need to find the derivative of…

Q: Plot the curve x³ + y3 = 6xy together with the tangent to the curve at the point

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Q: Determine the tangent to the curve 3y2 = x3 at (3,3) and calculate the area of the triangle bounded…

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Q: (b) Find the points on the curve y = 2x3 – 3x2 – 12x + 20 where the tangent is parallel to the…

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Q: The x-coordinate of the point where the tangent line to the parabola y=2x^2 at x=1 intersects the…

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Q: Find the equation of the tangent line to the curve at the given point. y = 9x – 8/x, (1, 1) %3D

A: Given,           Equation of the curve is y = 9x -8x  and point = (1,1)

Q: Find an equation of the tangent line to the curve at the given point

A: We have given the curve y = x5 + 3e5 and the point (0, 3). Find the slope at x = 0. Therefore, we…

Q: a. Determine the points where the curve 4x + 5y - y = 6 has a vertical tangent line. b. Does the…

A: a)  curve is 4x+5y2-y=6         Slope of tangent line is m=dydx    Differentiate the above equation…

Q: Find an equation of the tangent line to the curve at the given point y = x³ – 3x + 1, (2,3)

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Q: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

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Q: At what point is the tangent line to the curve y = 2x perpendicular to the line x – - 2y – 8 = 0? -…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: Given that  x=t^3+1,y=t^4+t  To find the equation of the tangent line

Q: Find equation of the tangent line to the curve at the following point.

A: To write an equation for tangent line to the curve at a given point, we calculate the slope at the…

Q: Find an equation of the tangent to the curve at the given point. (1) X²+4xy-y²-4x=1, (1,2) (2)…

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Q: find an equation for the tangent line to the graph of y=(5-2x)^2 at (3,1).

A: Explanation of the answer is as follows

Q: Find the equation of the tangent and length of the tangent to the curve y= x2+1 at (1,2)

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Q: Find the coordinates of the point in the first quadrant at which the tangent line to curve…

A: Find the coordinates of the point in the first quadrant at which the tangent line to curve…

Q: Find an equation of the tangent line to the curve at the given point. y = 3x - 14x + 1, (5, 6)

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Q: At what point is the tangent line to the curve y³ : = 6x² perpendicular to the line 2x + y = 2 = 0?…

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Q: For the curve whose equation is given by x2 - 3xy + y2 - 4x + 2y +1 = 0, find the slope of the…

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Q: Find an equation of the tangent line to the curve at the given point. y = 4*, (0, 1)

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Q: Find the coordinates of a point on the parabola y=−x² where the slope of the tangent is 5. x+3x+4

A: The given parabola is y=-x2+3x+4 We need to find the coordinates of the point on this parabola where…

Q: The curve given by the equation y^2=x^3+3x^2 is called the Tschirnhausen cubic. Find all values of x…

A: The curve is given by the equation y2=x3+3x2. The graph of the given function is drawn as

Q: Find an equation of the tangent line to the curve at the given point. y = x3 - 2x + 1, (3,22)

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Q: Determine the equation of the tangent line to the graph of y = y2 – x² at the points (분 ) and (블, )

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Q: . Determine the points where the curve 6x+ 4y-y=6 has a vertical tangent line. p. Does the curve…

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Q: a. Determine the points where the curve 4x + 2y -y =1 has a vertical tangent line. b. Does the curve…

A: Consider the given curve 4x + 2y2 – y = 1