Consider a function \(f\) with \(f^1(X^*) = 0\) and \(f^{1l}(X^*) > 0\). Based on these conditions, determine the nature of the critical point \(X^*\) for the function \(f(X)\).
- \(X^*\) is a local maximum
- \(X^*\) is a local minimum
- \(X^*\) is a global maximum
- \(X^*\) is a global minimum
