Question

Find the maximum or minimum value of $f\left(x\right)=-3x^2+9x$

• A. $\frac{25}{4}$
• B. $\frac{23}{4}$
• C. $\frac{27}{4}$
• D. $\frac{29}{4}$

Answer 1

The correct option is C $\frac{27}{4}$

$f\left(x\right)=-3x^2+9x$ is a quadratic function with $a=-3$ and $b=9$.

Thus, the maximum or minimum value occurs at:

$x=-\frac{b}{2a}=-\frac{9}{2(-3)}=\frac{9}{6}=\frac{3}{2}$

Since $a<0$, the function has the maximum value

$f\left(\frac{3}{2}\right)=-3{\left(\frac{3}{2}\right)}^2+9\left(\frac{3}{2}\right)=-3\left(\frac{9}{4}\right)+\frac{27}{2}=-\frac{27}{4}+\frac{27}{2}=\frac{-27+54}{4}=\frac{27}{4}$