Question

Compare the right-hand and left-hand derivatives to determine whether or not the function is differentiable at the point
whose coordinates are given.

Answer 1

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) = 1 while limx->􀀏0- f' 􀆍(x) = 2, f(x) is not differentiable at x = 0.
C) Since limx->􀀏0+ f' 􀆍(x) = 2 while limx->􀀏0- f' 􀆍(x) = 1, 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.