For (1) and (2), use the mean value theorem on the intervals [1,2] and [0,1] respectively. Since a derivative always has the intermediate value property (Darboux's theorem), it follows that there is a between and where the derivative is 1/2.
For (1) and (2), use the mean value theorem on the intervals [1,2] and [0,1] respectively. Since a derivative always has the intermediate value property (Darboux's theorem), it follows that there is a between and where the derivative is 1/2.