CHT applies when the DP has form .
Rewrite your recurrence to extract the linear form. Identify , , .
Check if slopes or queries are sorted. If yes, use the simple deque. If not, use binary search or Li Chao tree.
Time:
Time complexity: for sorted case, for general case. CHT is effective because it doesn't require QI. It exploits linearity instead.
Space complexity: for the hull.