Question

The maximum value of $f\left(x\right)=100-|45-x|$ is

• A. $100$
• B. $145$
• C. $55$
• D. $45$

Answer 1

Answer: (A)

$100$

$f\left(x\right)=\{\begin{array}{cc}145-x& ifx>45\\ 55+x& ifx<45\end{array}$
$f^{\prime }\left(x\right)=\{\begin{array}{cc}-1& x>45\\ 1& x<45\end{array}$
$f\left(x\right)$ is maximum at $x=45$
$f\left(45\right)=100$