A function f(x) is said to be differentiable at x = a if:
A function f(x) is said to be differentiable at x = a if:
- A. LHL = RHL
- B. LHD = RHD
- C. f(a) is defined
- D. Both LHL = RHL and LHD = RHD
Answer: D) Both LHL = RHL and LHD = RHD
Explanation: Differentiability mathematically requires the Left Hand Derivative (LHD) to equal the Right Hand Derivative (RHD) as finite values, which inherently implies continuity (LHL = RHL = f(a)).
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