Find a cubic function  y = ax3 + bx2 + cx + d  whose graph has horizontal tangents at the points  (−2, 9) and (2, 3).

Q: Apply derivative to determine the vertex of the parabola y = x² + 2x + 2.

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Q: Find the equation of the tangent line to the parabola at the given point. x2 = 2y, (-5, ) 2у, %3D

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Q: Find an equation of the tangent line to the parabola y = x2 -1 at the point (2,3) y 4x-5 Oy - 4x - 9…

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Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

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

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Q: Find the orthogonal trajectories for the family of curves 6x² + y² -9ax=0.

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Q: Find the parabola y= ax2+bx+c that passes through (2,1) and be tangent to the line y=2x + 4 at (1,6)

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Q: Find all points (x, y) on the graph of f(x) = x - 3x + 8x + 23 with tangent lines parallel to the…

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Q: find the point (x,y) at which the graph of y=7x2+5x-6 has a horizontal tangent line.  The function…

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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 equation of tangent for the implicit function x3 - xy2 + 3y2 + 4 = 0. at the point (1, 2)

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Q: Find the equations of all tangent lines to the curve x² + 4y2 = 8 that pass through the %3D point…

A: The curve x2+4y2=8 that pass through the point (-4, 0). We have to find the equation of all tangent…

Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 6x – 3, at which the slope of the tangent…

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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: When we are standing at the point (1,-3), the function f(x, y) = 3x²y+xy is increasing most rapidly…

A: We have to find the direction of  rapid increase of the function using gradient of the function.

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 point on the curve y = /2x + 3 which is closest to the point (5, 0).

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Q: Find the parabola with equation y= ax2 +bx whose tangentline at (1, 1) has equation  y= 3x -2.

A: We have to find equation of parabola y=ax2+bx which has tangent y=3x-2 at 1,1 .

Q: I dont know where to start this problem. It would be great to have some help

A: Given:

Q: Find the point (xo,yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent line…

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Q: Find an equation of the tangent line to the parabola y − x2 - 8x + 9 at the point (3, -6).

A: The derivative of a curve at a point gives the slope of the tangent to the curve. It can be…

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 point on the ellipse x^2+2y^2=1  where the tangent line has a slope of 1.

A: We know, slope of tangent line = dydx

Q: Find the point (xo, Yo) on the graph of y = x³ + 3x² + 5x – 3, at which the slope of the tangent…

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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).

A: To Determine: FInd the equation of tangent plane to the graph of…

Q: - Find the equation of the tangent to the 2(x2 + y²)² = 25(x² - y2) %3D at (3,1)

A: According to the problem, we have

Q: Find the point (xo, yo) on the graph of y = x + 3x² + 4x – 5, at which the slope of the tangent line…

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: What is the slope of the tangent line to the graph of any quadratic function of the form y=ax²+bx+c…

A: First find the vertex of the parabola, y=ax2+bx+c . Then, compute the expression for dydx .…

Q: Find the point (xo, yo) on the graph of y = x³ + 3x? + 8x – 3, at which the slope of the tangent…

A: To find the slope of the function we need y'y=x3+3x2+8x-3y'=3x2+6x+8

Q: Find an equation of the tangent line to the parabola y=x2  -8x+9 at the point (3, -6)

A: Given :          y= x2-8x+9

Q: At what point on the parabola y =  3 x2+ 2x is the tangent line parallel to the line y = 10x −2? Use…

A: First prinicipal : dydx=limh→0f(x+h)-f(x)h

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 cubic y = ax3 + bx2 + cx + d that passes through the points (-1, -10) and (1, -4) and tangent to…

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Q: Find the point (x0,y0) on the graph y=x^3 + 6x^2 +3x -5 at which the slope of the tangent line has…

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Q: find all points (x,y) on the graph of f(x)=3x^2-5x with tangent lines parallel to the line y=7x+1.

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Q: Make the curve y=ax²+bx+ c pass through (2,1) and be tangent to the line y=2x+4 at (1,6)

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Q: Find the point (xo, yo) on the graph of y = x + 9x2 + 3x - 4, at which the slope of the tangent line…

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Q: Find the equation of the line tangent to the graph of f(x) = 5x° +4x² – 5z – 6 at z = -6. %3D

A: Given that       f(x) = 5x3+4x2-5x-6      at x=-6 Here we have to find the equation of the line…

Q: Find the gradient of the curve . Y=4x^2 at x=3

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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: Determine the co-ordinates of all the points at which the tangent to the curve y = 3x'e8x is…

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

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: Find the orthogonal trajectories of the family of curves x3y-xy3=c where c is constant

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Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

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Q: Find a cubic function y = ax3 + bx2 + Cx + d whose graph has horizontal tangents at the points (-2,…

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Q: At what point of the parabola y=x -3x+5 is the tangent line parallel to the line 3x-y 2?

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Q: Find the cubic function y = ax³ + bx² + cx + d where its graph has horizontal tangent line at (-2,6)…

A: solve the given problem.

Q: Find the point (xo, yo) on the graph of y = x' + 9x² + 7x – 5, at which the slope of the tangent…

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Q: Find an equation of the tangent plane to the surface at the given point. + 3x – z2 = 56, (5, -3, 2)

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