Question

If $f\left(x\right)=x^2+kx+1$ is monotonic increasing in $[1,2]$ then the minimum values of $k$ is-

• A. $4$
• B. $-4$
• C. $2$
• D. $-2$

Answer 1

The correct option is D $-2$

$f\left(x\right)\ge 0$ for monotonically increasing.
$2x+k\ge 0$
$k\ge -2x$
Now it is increasing in the interval $[1,2]$
Hence
$k\ge -2$ and $k\ge -4$
Hence
From both we get
$k\ge -2$
Hence minimum value of k is $-2$