Bacon believes that the medical profession should be permitted to ease and quicken death where the end would otherwise only delay for a few days and at the cost of great pain.

The context indicates that the action would be completed at some point in the future i.e. the patient will have passed away at some point in the future. Hence, the correct tense to use in this case is the future perfect tense i.e. 'would be delayed'. The sentence gives two reasons for administering quick death and hence these two reasons should be separated by the conjunction 'and'. From the context, we can infer that there will be a delay of a few days if quick death is not administered by the doctor. Hence, a negative conjunction like otherwise is needed for the sentence to make sense. Hence, option C.