Simple Question? (1 Viewer)

[Lemiixem]

Find the equation of the curve passing through (1,4) if its gradient function if given by y = x^3 - 3x^2 + 5

 

[Timske]

Find the equation of the curve passing through (1,4) if its gradient function if given by y = x^3 - 3x^2 + 5

Find the primitive of the curve
f ' (x) = x^3 - 3x^2 + 5
:. f (x) = x^4/4 -x^3 + 5x + c
You know it passes through the point (1 , 4)
4 = 1/4 - 1 + 5 + c
4 = 4.25 + c
c = -1/4
:. equation of the curve is y = x^4/4 -x^3 + 5x -1/4