Let f(x) = { x² + 2, x ≤ 1; 3x, x > 1 }. At x = 1, f is: A. continuous but not differentiable B. differentiable C. discontinuous D. neither continuous nor differentiable Answer: A) continuous but not differentiable Explanation: LHL = 1²+2 = 3, RHL = 3(1) = 3, f(1) = 3, continuous. LHD = 2x at x=1 is 2, RHD = 3, not equal, so not differentiable.

imo class 12 continuity and differentiability

Let f(x) = { x² + 2, x ≤ 1; 3x, x > 1 }. At x = 1, f is:

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Let f(x) = { x² + 2, x ≤ 1; 3x, x > 1 }. At x = 1, f is:

Answer: A) continuous but not differentiable

Explanation: LHL = 1²+2 = 3, RHL = 3(1) = 3, f(1) = 3, continuous. LHD = 2x at x=1 is 2, RHD = 3, not equal, so not differentiable.