consider dy/dx = 2-2y where y=f(x) is the particular solution to the differential equation where f(0)=2.

Question

1. write an equation for the line tangent to f at x=0
2. is f concave up or down at (0,2)?
3. find f(x)

Answer 1

The point (0,2) lies on the curve, so the tangent there is
y-2 = -2(x-0)

y" = -2y'
y' = -2, so y" > 0
so the graph is concave up

see what you can do with the last part.