## Using the Definition to Compute the Derivative - Exercise 2

Exercise 2. Discuss the differentiability of Answer. May be the scariest thing about this function is the absolute value. So the best thing to do is to look for ways to remove it. Therefore we are led to find out when x2 - x is positive or negative. We get Clearly the derivative exists at every point, except maybe at 0 and 1. Let us discuss these two points. Let us start with 0. We have Since the function is defined differently from the left and the right of 0, then we have to consider the limits to the left and to the right at 0. We have and This implies that f'(0) does not exist. Similar computations will also give and which implies that f'(1) does not exist.

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