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Teacher
Math · Personal teacherMinimum of a quadratic · 0 ≤ x ≤ 3
- Student: Why is the minimum not 0?
- Teacher: The endpoints give 0, but there may be a smaller value between them. Can you complete the square?
- Student: It is (x − 2)² − 1. At x = 2, the value is −1!
- Teacher: Exactly. Since x = 2 is in the interval, compare the vertex with both endpoints.
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Solution analysisIllustrative practice questionx + 4/xx > 0
Find the minimum value of this expression.
My work
By the AM–GM inequality
x + 4/x ≥ 2√4 = 4
∴ The minimum is 4Check needed
Submitted answer4
AI mentoring
Why is a check needed if my answer is correct?
Revised reasoningx + 4/x ≥ 2√4 = 4Equality holds when x = 4/x, so x = 2
Since x = 2 satisfies x > 0, the minimum is 4
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