Question

Consider the function $y=x^2-6x+9$. the maximum value of $y$ obtained when $x$ varies over the interval $2$ to $5$ is

• A. $1$
• B. $3$
• C. $4$
• D. $9$

Answer 1

The correct option is C $4$

$y=x^2-6x+9,\frac{dy}{dx}=2x-6,\frac{d^{2}y}{d{x}^2}=2$
Put $\frac{dy}{dx}=0\Rightarrow x=3isthecriticalpointand{f}^{\prime \prime }\left(3\right)=2>0$
$\therefore f\left(x\right)$ has a minimum at $x=3$
Hence Maximum value of $y$ occur at corner points
i.e., $y\left(2\right)=1,y\left(5\right)=4$
$\therefore$ The maximum value of $y=4$