16Hit1600
Advanced MathHardLeast value of a quadratic on a restricted interval

Advanced Math practice question

The function f is defined by f(x) = x² − 6x + 10. What is the least value of f(x) for 0 ≤ x ≤ 2?

Answer: 2

The vertex is at x = 3, outside the interval, and f decreases across 0 ≤ x ≤ 2. So the least value is at x = 2: f(2) = 4 − 12 + 10 = 2.

Common wrong answers

If you answered 1
1 is the minimum over all real x (at x = 3), but 3 is outside the interval.
If you answered 3
3 is the x-coordinate of the vertex, not a value of f.
If you answered 10
10 is f(0), the greatest value on the interval.

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