Question

What is the maximum value of the function $f\left(x\right)=2x^2-2x+6$ in the interval $[0,2]$?

• A. $64$
• B. $\frac{64}{3}$
• C. $10$
• D. $\frac{128}{4}$

Answer 1

The correct option is B $\frac{64}{3}$

For critical points:
$\frac{dy}{dx}=0$
i.e., $f^{\prime }\left(x\right)=4x-2=0\therefore x=\frac{1}{2}$
$f^{\prime \prime }\left(x\right)=4>0$
$\Rightarrow f\left(x\right)$ is minimum at $x=\frac{1}{2}$
So maximum value occurs at boundaries
$f\left(0\right)=6,f\left(2\right)=10$
$\therefore$ Max value $=10$