Continuity and Differentiability · Class 12 · CBSE · Science Mathematics
The function f(x) = ax + b for x ≤ 1 and f(x) = x² for x > 1 is both continuous and differentiable at x = 1. What are the values of a and b?
Practice question from Continuity and Differentiability (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · MCQ · Q-107B7C
The function f(x) = ax + b for x ≤ 1 and f(x) = x² for x > 1 is both continuous and differentiable at x = 1. What are the values of a and b?
- A.a = 1, b = 0
- B.a = 2, b = -1Correct answer
- C.a = -2, b = 3
- D.a = 2, b = 1
Solution
Continuity at gives . Differentiability gives equality of the derivatives: . Therefore, .
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