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For the piecewise function g(x) = { k√(x+1), 0 ≤ x ≤ 3; mx + 2, 3 < x ≤ 5 }, if g is differentiable, what is the value of k + m?
- 10/3
- 4
- 2
- 16/5
Correct answer: 2
Solution
For the function g(x) to be differentiable at x = 3, both the function values and their derivatives must match at that point. Solving the equations derived from the continuity and differentiability conditions leads to the conclusion that k + m equals 2.
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