Your answer should be c=(2/3)

The reasoning is that if the function were to be continuous, it would need to be a solid line with no holes in it. (Mathematics has a more complicated definition)

So you take both functions:

cx^2+2x=x^3-cx

x(cx+2)=x(x^2-c)

cx+2=x^2-c

cx+c=x^2-2

c(x+1)=x^2-2

c=(x^2-2)/(x+1)

Now since you know the function will meet at x=2, you can sub in 2 for x

c=(2^2-2)/(2+1

c=2/3

You can check the work on a TI-83 graphing calculator and see that both functions meet at x=2.