What is the least value of $a$ for which $f(x) = x^2 - 2ax + 3$ is decreasing on $(1, 2)$ ?

-2

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1

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2

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4

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$f'(x) = 2x - 2a \le 0$ must hold for every $x$ in $(1, 2)$ , that is $a \ge x$ there.
$x$ comes as close to 2 as we like, so $a \ge 2$ ; the least value is 2.

Worth noting

1 uses the left end only; at $x$ near 2, $2x - 2$ is positive and the function rises.

Ten questions from Increasing & Decreasing Functions, at your own pace.

Ten questions from Increasing & Decreasing Functions, at your own pace.

What is the least value of aaa for which f(x)=x2−2ax+3f(x) = x^2 - 2ax + 3f(x)=x2−2ax+3 is decreasing on (1,2)(1, 2)(1,2)?