Question

The maximum value of $f\left(x\right)=-3x^2+5x+2\forall x\in [0,2]$ is

• A. $\frac{150}{36}$
• B. $\frac{150}{36}$
• C. $\frac{147}{36}$
• D. $\frac{210}{36}$

Answer 1

The correct option is C

$\frac{147}{36}$

$f\left(x\right)=-3x^2+5x+2$

Here $a<0\Rightarrow$ graph is inverted cup shaped & maximum value will occur at $x=\frac{-b}{2a}=\frac{5}{6}$
As $0<\frac{5}{6}<2$
$\Rightarrow$ No other value of $x$ in $[0,2]$ will have
$f\left(x\right)>f\left(\frac{5}{6}\right)$
So, $f\left(\frac{5}{6}\right)$ is the maximum value.
$f\left(\frac{5}{6}\right)=-3x{\left(\frac{5}{6}\right)}^2+5\left(\frac{5}{6}\right)+2=\frac{147}{36}$