The first derivative is correct. Since it is a second-degree polynomial, the second derivative must be a first-degree polynomial.

f(x) is increasing when f'(x) > 0 and it is decreasing when f(x) < 0. You need to solve a quadratic inequality. Similarly, f(x) is convex when f''(x) > 0 and f(x) is concave when f''(x) < 0.