Answer:
Option (3)
Step-by-step explanation:
Given function is,
f(x) = 3x² - 2x
= [tex]3(x^{2} -\frac{2}{3}x)[/tex]
= [tex]3(x^{2} -\frac{2}{3}x+\frac{1}{9}-\frac{1}{9})[/tex]
= [tex]3(x^{2}-\frac{2}{3}x+\frac{1}{9})-\frac{1}{3}[/tex]
= [tex]3(x-\frac{1}{3})^2-\frac{1}{3}[/tex]
Vertex of the parabola → [tex](\frac{1}{3},-\frac{1}{3})[/tex]
Here, leading coefficient is positive (+3),
Therefore, parabola will open upwards.
In a parabola opening upwards function decreases from negative infinity to the x value of the vertex.
Function will decrease in the interval (-∞, [tex]\frac{1}{3}[/tex]).
Option (3) will be the answer.
