What is the least value of $a$ for which $f(x) = x^2 + ax + 5$ is increasing on $(2, 3)$ ?

-6

Correct answerYour answer

-5

Correct answerYour answer

-4

Correct answerYour answer

4

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$f'(x) = 2x + a$ must be $\ge 0$ for every $x$ in $(2, 3)$ .
The smallest value of $2x + a$ there is just above $4 + a$ , so we need $4 + a \ge 0$ : $a \ge -4$ , and the least value is $-4$ .

Worth noting

$-6$ uses the right end, $x = 3$ ; the condition must hold at the left end too, where $2x + a$ is smallest.

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+ax+5f(x) = x^2 + ax + 5f(x)=x2+ax+5 is increasing on (2,3)(2, 3)(2,3)?