Hint: The definition of concave up is when d^2y/dx^2 > 0. From here:
Second derivative test - Wikipedia, the free encyclopedia
You are looking at the sign of the second derivative at a point (or an interval as you are doing).
Don't look at the concavity of the 2nd derivative: just look at the sign of the derivative.
Also note that a function can have segments that are both concave up and concave down in different regions.