For the function $f(x)=x^2+ax+1$ to be increasing on $[1,2]$, the valu…

Question

For the function $f(x)=x^2+ax+1$ to be increasing on $[1,2]$, the values of $a$ must satisfy

Accepted Answer

A. $a\ge -2$

1. $f'(x)=2x+a$.
2. For increasing on $[1,2]$, need $f'(x)\ge 0$ for all $x$ in $[1,2]$.
3. The minimum of $2x+a$ occurs at $x=1$: $2(1)+a\ge 0$.
4. So $a\ge -2$. The trap $a\ge -4$ wrongly tests at $x=2$.
_Source: NCERT Class 12 Mathematics Ch 6 "Application of Derivatives", p.12_

Answer

$a\ge -4$

Answer

$a\le -2$

Answer

$a\le -4$