Question

find the equation of a curve for which y''=6x-6 if the curve has a critical point at (2,1).

Answer 1

d^2y/dx^2 = 6x - 6

dy/dx = 3x^2 - 6 x + c
that is zero at x = 2
3*4 -6*2 + c = 0
c = 0

y = x^3 - 3 x^2 + k
1 = 8 - 12 + k
k = 5
so
y = x^3 - 3 x^2 +5