Could a boredofstudies boffin tell me why answers to newtons method questions use the higher value? (e.g. zero between 3.7 and 3.8, 3.8 is used to estimate the positon of the zero.
1) The question usually gives you the initial estimation so you shouldn't need to choose it yourself.
2) The higher estimate might be because the question is implying that the root is closer to 3.8 than 3.7, hence an estimate of 3.8 would be better than 3.7.