Find all points (x, y) on the graph of f(x) = 1 - 4x + 20x + 4 with tangent lines parallel to the line 15x – 3y = 4. ..... The point(s) is/are. (Type an ordered pair. Use a comma to separate answers as needed.)

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A: Consider the function: yx=x3-2x2+x+1 Slope of a tangent at any point of a function is given by…

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A: Differentiate the equation x2y-2x+63y=2 wrt x:  ddxx2y-ddx2x+ddx63y=ddx22xy+x2dydx-2+63dydx=0

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A: Given : The two curves x2 - y2 = c and xy = d intersect at point P where c and d are constants.…

Q: Show that if P lies on the intersection of the two curves x2 − y2 = c and xy = d (c, d constants),…

A: Solution:Givenx2-y2=c     and   xy=dTo prove tangent curve at P are…

Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 15x + 10 with tangent lines parallel to the…

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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: Find the value of c such that the line y = (1/6)x + (3/2) is tangent to the curve y = c(sqrt(x)).

A: Solution: Y1=16x+32Y2=cx

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Q: *(x, y) = xe"

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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.

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

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

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A: Consider the given equation of curve, x+y=cddxx+y=ddxc12x+12ydydx=012ydydx=-12xdydx=-yx Therefore,…

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A: Given information: There are two equations  are y1=-x2+ax+b, y2=x2+cx-2 have a common tangent line…

Q: Find all points (x, y) on the graph of f(x) = x° - 4x + 20x + 11 with tangent lines parallel to the…

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Q: find an equation of the tangent plane at the given point. f (x, y) = x2 + y−2, (4, 1)

A: To find equation of tangent plane at (4,1)

Q: Let a(t)-(1+t,t?,2+t?), then the equation of the tangent line at t-1 is: (2+t,-1+2t,3+2t)…

A: Here, a'(t)=(1,2t,2t)a'(1)=(1,2,2)anda(1)=(2,1,3)

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

A: Mentioned below is the answer

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A: The formula to find the equation of a tangent plane at a point (a, b) to a given surface f(r,  s) is…

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A: Given  y=ax2-6x+1find derivativey'=ddx(ax2-6x+1)y'=2ax-6+0y'=2ax-6at x = 1y'=2a(1)-6y'=2a-6

Q: Given the function z = = f(x,y) = 2y³ -5xy-3x²+2, find the equation of the tangent plane at (1,-1),…

A: Given problem:- Given the function z  = f(x, y) = 2y³ −5xy-3x²+2, find the equation of the tangent…

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Q: %3D %3D .2 ,2.

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Q: Find an equation of the tangent plane to the graph of f (x, y) =2x2 - 4xy 2 at (-1, 2)

A: Given: f(x, y) = 2x2 -4xy2  To find: Equation of tangent plane to the graph of  f(x, y) = 2x2 -4xy2…

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Q: OShow that every point (b, c) in the plane lies on a tangent line to the graph of y = x³.

A: Consider the given information. y=x3 Find the derivative of the function. dydx=ddxx3y'=3x2

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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).

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Q: 11. Find all points (c, f(c)) 9. on the graph of f(z)= x³ – 3x² where the tangent line has slope

A: Given,       f(x) = x3 - 3x2       slope = 9

Q: Find an equation for the tangent plane to the graph of the function f (x, y) = y In(x² + 2y) + xy at…

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Q: Find all points (x, y) on the graph of y = with tangent lines perpendicular to the (x- 6) line y= 6x…

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Q: Find the equations of the tangent lines in both the x-direction & the y-direction to the function z…

A: We need to find equation of tangent line.

Q: Find the tangent plane to the equation z = x2 + 5y² + 3y at the point (-5,-2,39)

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Q: b) Let f(x) = 4x - 2x - 5. %3D Find the intersection of the tangent line at c = 2 with the x axis.…

A: Given: The function fx=4x3-2x-5, To find: The intersection point of the tangent line at c=2 with…

Q: 7. Let f(x,y) = x²y+ry. Find an equation of the tangent plane to the graph of f at the point…

A: The detailed solution is given below Thank you

Q: If f(2) = -3, f'(2) = ÷ and g(x) = f¯(x), what is the equa %3D the tangent line to g(x) at x = -3?…

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Q: The tangent line to the graph of y = In(2x) is perpendicular to a + 4y = 1 at the point where Select…

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