determine the equation of the curve if it passes through the point (-2,4)

Question

The gradient of the tangent drawn at any point in a curve us given by m= dy/dx = 1-4x

Answer 1

The gradient of the tangent drawn at any point in a curve us given by m= dy/dx = 1-4x

integrate the derivative dy/dx = 1 - 4x.

Integration gives us,

 y = x - 2x^2 + const

We are told thsat it passes through the point (x,y) = (-2, 4)

Therefore x = -2 and y = 4 satisfy the equation of the curve above.

Substituting fior x = -2 and y = 4 into the equation y = x - 2x^2 + const,

4 = -2 - 2(-2)^2 + const

4 = -2 -2*(4) + const

6 = -8 + const

const = 14

The equation of the curve then is: y = x -2x^2 + 14