Compare the right-hand and left-hand derivatives to determine whether or not the function is differentiable at the point whose coordinates are given.
y = xy = 2x
A. Since limx?0+ f '(x) = 2 while limx?0- f '(x) = 1, f(x) is not differentiable at x = 0.
B. Since limx?0+ f '(x) = -2 while limx?0- f '(x) = -1, f(x) is not differentiable at x = 0.
C. Since limx?0+ f '(x) = 1 while limx?0- f '(x) = 2, f(x) is not differentiable at x = 0.
D. Since limx?0+ f '(x) = 1 while limx?0- f '(x) = 1, f(x) is differentiable at x = 0.
Answer: A
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