Question

A differentialbel function $f\left(x\right)$ has a relative minimum at $x=0$, then the funciton $y=f\left(x\right)+ax+b$ has a relative minimum at $x=0$ for

• A. All $b>0$
• B. All $a>0$
• C. All $b$ if $a=0$
• D. All $a$ and all $b$

Answer 1

The correct option is C All $b$ if $a=0$

Clearly when $a=0$, the natrue of the function $f\left(x\right)$ is same as that of $f\left(x\right)+b$.