Find the curve whose slope at the point (x, y) is x' +2x² – 7x +9 if the curve is required to pass through the point (-2, 5).

Q: Find the slope of the tangent line to the curve 4x2 – 2xy – y = 32 at the point (2, – 2).

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Q: Find the solution of the equation y= 2x -x- 10 in the interval (2, 4] using derivatives. You can use…

A: To solve an equation  f(x)=0 using derivative of function, we can use the formula…

Q: Find the slope of the line tagent to the curve of y = In x/x at point (1,0)

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Q: Find an equation of the tangent line to the curve y = x - 3x + 5x that has the least slope.

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Q: Find the line tangent to the curve x + y3 = 4 at the point (3/3, –1).

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Q: Find an equation of the tangent line to the curve y=2x^2+3 that is parallel to the line 8x-y+3=0

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Q: Find the equation of a curve passing thorugh the point (0,2) and having slope x +ex-sinhx at any…

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Q: The slope of the tangent line to the curve y=2x^3 at the point (-4,-128) is ____. The equation of…

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Q: The slope of the tangent line to the curve y 2x at the point 2, 16) is:

A: As we know that; The slope of the tangent line to the curve is equal to the derivative of the…

Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

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Q: The equation of the tangent line to the curve x2 + y = 9, at (6,-16) is %3| 16 y = (x + 6) – 16 6 6…

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Q: Find the slope of the tangent line to the curve 4x + 4cy- 4y° 276 at the point (- 1,4).

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Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

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Q: Find the equation of the line passing through the point (4,5) and perpendicular to the line y= x+2…

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Q: Find the point where the line tangent to y=x* – 3x² +2 at (2, 6) crosses the x – axis.

A: y=x4-3x2+2,  2, 6 Differentiating with respect to x, we get dydx=4x3-32x+0=4x3-6x Now slope of the…

Q: Find an equation of the form y = f(r) for a curve with z-intercept 2 whose tangent line at any point…

A: we have to find an equation of the form y=f(x) for a curve with x-intercept 2 whose tangent line at…

Q: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

Q: Find the slope of the tangent line to the curve - 4x² + 4xy - 1y³ = - 148 at the point (3, 4).

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Q: Find the line tangent to the curve x 3 + y 3 4 at the point (-3/3, –1). V3 y = 3 x – 4 V3 4 - 3 -V3…

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Q: Find the line tangent to the curve x + yi = 4 at the point (3V3, –1). y = x- 4 Oy = x+4 y = O y= s…

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Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: Find the equation of the tangent plane to the graph of 9y f(x, y) = at the point (4, –-1). (Use…

A: The Equation of the tangent plane: - z0=(x0,y0) is a point in the domain of f, and defined by a…

Q: Find an equation of the line tangent to the curve defined by " + 5xy +y = 68 point (2, 2) at the

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Q: Find the curve in the xy-plane that passes through the point (9,4) and whose slope at each point is…

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Q: Find the slope of the curve y = 2x(x-1)° at point (1,-1). %3D O -1 O 4 O 2 O -2 O 1

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Q: Find the equation of line tangent of y=x4-2x2+1 at (2,9)

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Q: The slope of the tangent line to the parabola y 4x + 7x + 5 at the point (0, 5) is: The equation of…

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Q: Find the curve y = ƒ(x) in the xy-plane that passes through the point (9, 4) and whose slope at each…

A: Given, the curve y = ƒ(x) in the xy-plane that passes through thepoint (9, 4) and whose slope at…

Q: Find an equation for the tangent line to the curve y = xV 2x² - 14 at the point (3,6). O y- 6 = 14(x…

A: The equation of the tangent line to the curve is, y - 6 = 11(x - 3)  The detailed solution is as…

Q: There are two lines passing through the point (5,-1) that are tangent to the parabola y = -x^2+4x.…

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Q: Find the equation of a that has a y" = 4 if it has a slope of of 3 Curve Second derivative %3D at…

A: equation of the curve  is given below...

Q: 3 at the point 7, 3 is: The slope of the tangent line to the curve y %3D

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Q: Find the equation of a curve going through the point (3, 7) and having slope 4x² – 3 at (x, y).

A: Given ,Slope of curve is 4x2-3Thereforedydx=4x2-3Taking integationon both…

Q: 2. What is the slope of the line tangent to the curve 8x3 –- y² = 4 at the point (1,-2)?

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Q: 8. Find the point on the curve y = √2x 3 from the point (1, 4)-

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Q: Find the length of the curve (Sketch and Solve) One branched of the curve 9y2=4x3 from x = 0 to…

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Q: Please show me the partial derivatives for this homogenous equation and solve for GS/PS using Test…

A: Exact differential equation

Q: Find the curve in the xy-plane that passes through the point (4,8) and whose slope at each point is…

A: The curve in the xy-plane that passes through the point (4 , 8 ). Slope at each point is 3√x . We…

Q: x2/3 - y2/3 -y=1 ;(1, -1)

A: firstly we find the slope(m) by differentiate w.r.t. x  and then put the slope in equation of tanget…

Q: The line that is normal to the curve x + 3xy - 4y² = 0 at (3,3) intersects the curve at what other…

A: Given: x2+3xy-4y2=0 at (3,3)

Q: Find the equation of the line tangent to the curve y =8/x2+4 at the point (2, 1).

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Q: Find an equation of the curve that passes through the point (0, 2) and whose slope at (x, y) is x/y.

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Q: Find an equation of the curve that passes through the point (0, 4) and whose slope at (x, y) is x/y.

A: Solution:find the equation of curuepasses through the point (0,4)slope of cwue is xydydx=xyy dy=x…

Q: The slope of the tangent to the curve yx + y²x² -6 at (2,1) is

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Q: Determine the equation of the line tangent to y = /1+x³ at the point (2, 3).

A: The given function is y=1+x3. Its derivative is obtained as, dydx=ddx1+x3=121+x3ddx1+x3=3x221+x3 at…

Q: Find the x-coordinates of all points on the curve y = 12x" - 96x° - 168x + 26x + 91 where the…

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Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: y 1-

A: The solution is given below in the next step:

Q: The slope of the line tangent to the curve y=2x- 3 at point (1,-1) is 5

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