Question

Find the least value of $k$ for which the function $x^2+kx+1$ is an increasing function in the interval $1<x<2$.

• A. $1$
• B. $-1$
• C. $2$
• D. $-2$

Answer 1

The correct option is D $-2$

$f\left(x\right)=x^2+kx+1$

$f^{\prime }\left(x\right)=2x+k{f}^{\prime }\left(x\right)\ge 0$

$2x+k>02x>-kx>-\frac{k}{2}$

but $x\ge 1$

$1=\frac{-k}{2}$

$k=-2$