Question

What value of x will give the minimum value of $x^2$ - 4x + 7?

• A. x $\ge$ 3
• B. x = 2
• C. x < 2
• D. x = 0

Answer 1

The correct option is B x = 2

Suppose y = $x^2$ - 4x + 7
For minimum value of y, $\frac{dy}{dx}$ must be 0.
$=\frac{d}{dx}\left(x^2\right)-4\frac{d\left(x\right)}{dx}+\frac{d\left(7\right)}{dx}=0$
2x - 4 + 0 = 0
2x = 4
x = 2
Alternate Method:
For minimum, value of x $=\frac{-b}{2a}$
$\therefore x=\frac{4}{2\times 1}=2$