The Tschirnhausen cubic is the curve given by the equation x2 = y3 + 3y?. At which point(s) (x, y) on the curve is the tangent line horizontal? Show all of your work.

Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

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Q: Determine the equation of the tangent line and the quadratic approximation to the function z = e2"…

A: Given function is: z=e2x To find the equation of the tangent at a point x=x0 to curve y=fx,…

Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² – 7xy2 at the point (7, 8) z =

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Q: Find an equation of the tangent plane to the graph of f(x, y) = In(4x² – 2y2) at the point (1, 1). z…

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Q: Find the equation of the tangent to the curve xy2 + y³ = 6x + 3y at (1,2)

A: The curve is given as x y2 + y3 = 6x + 3y, the objective is to find the equation of tangent line at…

Q: Consider the curve defined by the equation y3+xy+2=0.  Show that there are no points on this curve…

A: Consider the given curve define by the equation:

Q: Consider the curve defined by the equation y³ + xy + 2 = 0. Show that there are no points on this…

A: Given Equation of curve   y3+xy+2=0  ---(1)

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

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Q: find the tangent line to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: Given the parabola x+2y2+2x-y-3=0..............i  Determine the slope of given line x-4y=2…

Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: Find the equation of the tangent plane to z at (-4,2).

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Q: a point on the cor ve y=x² - 2x -3 at which is parallel to Find the tangent line the X-axis

A: Given query is to find the the point where tangent line paray to x axis.

Q: Find the tangent plane to the equation z = 2x – 3y + y at the point (1, 2, – 8). -

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Q: Find the equation of the tangent line drawn to the curve y4−4x4−6xy=0 at the point M(1,2).

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Q: Find an equation of the tangent plane to the surface at the given point. 2 x2 + 2z?ey - x = 33, P =…

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Q: 2 2 18. At how many points on the curve + yš =1 in the TY-plane does the curve have a tangent line…

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Q: Find an equation for the tangent line to the parabola y = x² at the point P(1, 1). A y=2 B) y = x…

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Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

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Q: Find the equation of the tangent plane to the surface y = 2a2- z2 at the point (0,-1, 1)

A: Here is the solution

Q: Find the equation of the tangent plane to z = In(x²y) – x/y at (-;4).

A: Let x0,y0 be any point of surface function z=fx,y. Then the surface has a non vertical plane at…

Q: Find the tangent line to the curve x = -/t + 1 , y = , y = \3t at the point def ined by t = 3

A: Using formula of equation of tangent line to the curve at given point.

Q: The tangent plane to the graph of the function :==3y+1=(1+y} at the point (1; 1; 3/2) contains point…

A: The given equation of the surface is z=x2y+1. Rearranging the above equation gives, w=z-x2y-1 Find…

Q: Find an equation of the tangent plane to the graph of f(x, y) = 4x² - 7xy² at the point (7, 8). z =

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Q: d the equatiom of the tangent line to the curve xy – 7 = Vx + y² at the point (5,2).

A: For finding tangent line to the curve , find the derivative of the function and put the value of…

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: The tangent line to the curve ³ + y³ = 9xy at the point (4,2) intersects the y-axis at y = -1. -2.…

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Q: 46. Show that the sum of the x- and y-intercepts of any tangent line to the curve Vx + Jy = \c is…

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Q: Find an equation of the tangent line to the curve y? = x3 + 3x? at thu point (1, 2). 2у + 3x 3 3 3x…

A: We have to find the equation of tangent line.

Q: Find an equation of the tangent plane at the given point. g(x, y) = ely, (4, 1) (Express numbore in

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Q: Find an equation of the tangent plane to the graph z = Væ + y³ nt (8, 2, 4).

A: We know that equation of tangent plane to the graph z=f(x,y) at point (a,b,c) is…

Q: x² = y + 3y.

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Q: II. Find the equation of the tangent line to the curve z2+V#j+y² = 19 at the point (1, 4).

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Q: e, Find at the giren point on eauation Of the tangent live. to the corve. X=46",y=f'+|,(4,0)

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Q: If y-mx+B is thế équation of the tangent line to the curve X +2xy – y+ x = 39 at x=5 with a negative…

A: At x=5 we find y The points are (5, 1) and (5, 9)

Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: Find the equation of the tangent line to the function f(x) = 2x? – x at the point where x form y =…

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Q: Find a point on the graph where x = t² - 1, y = 2t has a vertical tangent.

A: For vertical tangents dx/dy=0

Q: 2i Find the eguation of the tangent: lime to tul Cur ve y=4x -x* at the point (l,3).

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Q: Find the equation for the tangent plane to the graph of h (x, y) = y sin (x y) + yª + 3 x² at the…

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Q: 4. Find the equation of the tangent plane to the level surface x4 + yz – yz² + 5x = 0 at 3

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Q: 2. The coordinates of the point where the curve y = Inx has a tangent with slope of e are: d. (e,-1)…

A: Slope is already given. And for slope we have to find dy/dx  and then simplify.

Q: The slope of the tangent to the curve y²x + y²a² = 6 at (2, 1) is A B) -1 в 14

A: We can find the slope of the tangent to the curve at the indicated point as below.

Q: Find the point on the curve y=/2 for which the tangent ine to the curve is perpendicular to the line…

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Q: Find the equation of the tangent plane to z=6x2+2y2  at the point (1,5)

A: Given  z = 6x2+2y2  at the point (1,5)

Q: The line y = -4x +b is a tangent line to the curve 3y²r + sin(2y – 4) = /(2y) at (a, 2).

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Q: Find the equation of the tangent plane to the surface y = 2x² – z² at the point (0,-1, 1)

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Q: 7.) Find an equation of the tangent plane to the surface, x y(2z-3), at the point P(4,4,2)

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Q: Find the equation of the tangent plane to the graph of xe*y- eyz = In(x?) at the point (1,1).

A: Solution