Question

Let $f\left(x\right)=\{\begin{array}{cc}|x^2-3x|+a,0\le x<\frac{3}{2}& \\ -2x+3x\ge \frac{3}{2}& \end{array}$ If f(x) has a local maximum at x =.

• A. $a\le 0$
• B. $a\le -\frac{9}{4}$
• C. $a\ge -\frac{9}{4}$
• D. $a=3$

Answer 1

The correct option is B

$a\le -\frac{9}{4}$

$f\left(\frac{3}{2}\right)=0\Rightarrow \underset{x\to \frac{3}{2}}{lim}|x^2-3x|+a\le 0\Rightarrow \frac{9}{4}+\le \Rightarrow a\le -\frac{9}{4}$