The interval in which the function f(x)=x^2-3x+7 is increasing, is

The correct answer is Option (2) → \( \left(\displaystyle\frac{3}{2},\infty\right) \)

f is increasing where f′(x) > 0.

    \( \displaystyle f'(x)=2x-3 \)

    \( \displaystyle 2x-3\gt 0\ \Rightarrow\ x\gt\frac{3}{2} \)

So f is increasing on \( \left(\frac{3}{2},\infty\right) \).

Shortcut: f is an upward parabola with vertex at \( x=-\frac{b}{2a}=\frac{3}{2} \); it decreases to the left of the vertex and increases to the right.