If f(x) = |x|³, then f(x) is:
If f(x) = |x|³, then f(x) is:
- A. continuous but not differentiable at x = 0
- B. differentiable at x = 0
- C. discontinuous at x = 0
- D. not defined at x = 0
Answer: B) differentiable at x = 0
Explanation: f(x) = |x|³. LHD at 0 = lim(h→0) |−h|³/h = −h² → 0. RHD = lim(h→0) h³/h = h² → 0. Both exist and are equal. So differentiable at x=0.
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