When t > 0 |t| = t
x = 2t - |t| = t > 0
y = t2 + t|t| = 2t2 y(0) = 0
When t < 0 |t| = -t
x = 2t - |t| = 3t < 0
y = t2 + t|t| = 0 y(0) = 0
Hence LHD =
[h]
[0+] {f(0-h) - f(0)}/(-h) = 0
RHD =
h][0+] {f(0+h) - f(0)}/h =
[h][0] 2h
2/h = 0
Simce LHD = RHD at x = 0 hence its differentiable at x = 0.
Moderation Team
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