(d) Assume the function has value 0 at . The graph eventually flattens out, indicating that the derivative at 0 is 0.
(b) (i) The one-sided limits are not equal, so the function is not continuous at 1. Since it is not continuous at 1, it is not differentiable at 1.
(c) (i) The one-sided limits at -1 both have value 5, so is continuous at 5. (ii) . The two one-sided limits of this expression are both -2, so is differentiable at -1 and the derivative is -2.
(a) does not exist, so is not continuous at 0.
(b) , so is continuous at 0. But , which does not exist, so is not differentiable at 0.
(c) , so is continuous at 0. , so is differentiable at 0.