Question

If $f\left(x\right)=\{\begin{array}{c}3x^2+12x+1,-1\le x\le 2\\ 37-x,2<x\le 3\end{array}$, then

• A. $f\left(x\right)$ is increasing in $[-1,2]$
• B. $f\left(x\right)$ is continuous in $[-1,3]$
• C. $f\left(x\right)$ is maximum at $x=2$
• D. all of the above

Answer 1

Answer: (C)

$f\left(x\right)$ is maximum at $x=2$

$f^{\prime }\left(x\right)=\{\begin{array}{c}6x+12,-1\le x\le 2\\ -1,2\le x\le 3\end{array}$

$(6x+12)\in [6,24]$

increases in $[-1,2]$

$f\left(x\right).$ is maximum at $x=2$