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Let f: R → R be given by
f(x) = { k - 2x, for x ≤ -1
{ 2x + 3, for x > -1
If x = -1 is a point where f attains a local minimum, then one possible value of k is
- 1
- -1
- 0
- 2
Correct answer: -1
Solution
For f to have a local minimum at x = -1, the left-hand limit (from the piece k - 2x) must equal the right-hand limit (from the piece 2x + 3) at that point. Setting these equal gives k - 2(-1) = 2(-1) + 3, which simplifies to k + 2 = 1, leading to k = -1.
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