Find the equation of the family of curves whose slope at any point (x,y) is 3x2+4

Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y =…

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Q: Determine the slope of the curve y =1/x+1 at point (−2,−1).

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Q: Find the equation of the line tangent to the graph of y = 2x - 8x2 + 2x -6 at x = 2. | %3D

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Q: Find the equation for the curve in the xy-plane that passes through the point (1, -1) if its slope…

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Q: Find the point of inflection of the curve y = x^3 - 6x^2 - x + 12. (-2,6) (2,-6) (-2,-6) (2,6)

A: We have to find point of inflection of given function.

Q: Find the equation of the line tangent to the graph of y = 4x (x - 4x + 5) at the point (2,8). y =

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Q: Find the relative maximum point of the curve: Y=16x+4x2-x4

A: Solution of question as follows

Q: What is the equation of the curve passing through the point (3,-2) and having a slope at any point…

A: We want to find correct option.

Q: Find an equation of the curve that passes through the point (1, 3), and has the given slope y′ =…

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Q: Find a parabola with equation y = ax2 + bx + c that has slope 8 at x = 1, slope -12 at x = -1, and…

A: To find a parabola with equation.

Q: Find an equation for the line perpendicular to the tangent to the curve y = x°- 16x + 6 at the point…

A: Given: y=x3-16x+6, 4,6 we know that equation of line which perpendicular to tangent at given point…

Q: Find the coordinates of the points on the curve y = x³ - 6x² + 14x – 12 at which the tangents have a…

A: We will differentiate with respect to x and equate the same to 5 and find the points.

Q: Find a parabola with equation y = ax² + bx + c that has slope 4 at x = 1, slope -16 at x = -1, and…

A: We know slope of a curve y=f(x) is given by, dydx=f'(x)

Q: Find an equation of the line tangent to thegraph of ƒ(x) = x3 + 4x at (1, 5).

A: Given: The graph is expressed as fx=x3+4x To Find : Equation of line tangent to 1,5  The equation of…

Q: The slope of the curve defined by the equation y-x + x =-2 at the point (-1,0) is %D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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

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Q: What is the equation of a family of curves orthogonal to 2x2 + y2 = c?

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Q: The slope of the curve y- xy- 3x = 1 at the point (0, -1) is а. 1 с. -1 b. 2 d. -2

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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 all points on the graph of ƒ(x) = x3 + 9x2 + 19x - 10 where the slope of the tangent line is…

A: The derivative of xn is nxn-1 for n≠0. The derivative of f(x)+g(x) is f'(x)+g'(x). The derivative of…

Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y = dy…

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Q: Find a possible point of inflection of the curve y x +3x2 + 6x

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Q: 4)Solve for the family of curves of straight lines with y-intercepts thrice as their corresponding…

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Q: Find the equation of the curve whose slope at any point X-2 3-y and passes through (-1, 1

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Q: Find all points on the graph of ƒ(x) = x3 + 9x2 + 19x - 10 where the slope of the tangent line is -5

A: Given: ƒ(x) = x3 + 9x2 + 19x - 10 The slope of the tangent line is -5

Q: 9. Find the equation of the line tangent to the curve y = 3x5 + 10x³ + 15x + 1 at its point of…

A: the given curve , y=3x5+10x3+15x+1 we have to find the equation of the tangent line to the given…

Q: Find the member of the curve whose slope at any point is 2e** and passes through the point (0, 1)

A: We need to find the member of the curve whose slope at any point is 2e^(4x) and passes through…

Q: Find the point of inflection of the curve x^3 – 3x^2 –x + 7.

A: For inflection point, second derivative is zero

Q: Find the slope of the curve at the given point. 2y5+9x9=7y+4x at (1,1)

A: The given curve is,

Q: Find an equation of the curve that passes through the point (1, 1), and has the given slope y′ = −…

A: y'=-9x16yPasses through (1,1)Formula∫xndx=xn+1n+1+C

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: ) Find the slope of the curve x +y3- 6x²y = 0 at x = 1

A: Slope of a curve: For non- linear functions, the rate of change varies along the given curve. So,…

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

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Q: Find the equation of the line tangent to the graph of f(x)= 7x³ +5z2 - 3z- 3 at z = -5. %3D

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Q: Find the equation of the curve that passes through (1,13) and having a slope of -4x at that point.

A: *given:- slope, dy/dx = -4x points (x, y) = (1, 13)   *to find:- equation of the curve.

Q: Find the equation of a line tangent to a circle whose equation is x2 + y2 – 4x - 21 = 0 at point…

A: Let's.

Q: Find an equation of the curve that passes through the point (8, 2), and has the given slope y′ =…

A: Solution:-We have to find an equation of the curve that passes through  the point (8,2) and having…

Q: Find the equation of the line tangent to the graph of y = 4x'-9x-7 at the point (1,8).

A: Method to find tangent at a point of any curve.

Q: Find the equation of the line tangent to the parabola y = x^2 -1 at the point (-2,3).

A: Given the parabola :

Q: Determine the slope-intercept equation of the line tangent to the graph of y = 4x^2 - 7x + 1 at x =…

A: y=4x2-7x+1 We need to Determine the slope-intercept equation of the line tangent to the graph of the…

Q: Find the following points of intersection.

A: Given that, y=42xy=2x2

Q: Find the equation of the family of curves whose slope at any point (x, y) is 2. y 4. equal to the…

A: We need to find the family of curves. NOTE - As per our guidelines we can not solve multiple…

Q: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection…

Q: What is the equation of the curve passing through the (1, 16) and having a slope at any point (x,y)…

A: Given- 2xyx2+3 To find- The equation the curve passing though the (1,16) and slope at any point x,y…

Q: Find the slope of the curve x3y3 + y2 = x + y at the points (1, 1) and (1, -1).

A: Given,

Q: Find the equations of the line tangent to the curve y = x³ + x , where the slope is equal to 4.

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Q: Find the equation of the line that is tangent to the graph of y= x^3 +4/x^2 at point (2,9)

A: The equation of tangent line to y=f(x) at (x0,y0) is y-y0=f'(x0)(x-x0)

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.