QuestionExample (2)
Investigate the sign of the following functions : i) $F(x)=x+5$ ii) $F(x)=-3 x+6$

Studdy Solution
Determine the sign of $F(x) = -3x + 6$ for intervals around $x = 2$:
- For $x < 2$, choose a test point, say $x = 0$: $$F(0) = -3(0) + 6 = 6$$ Therefore, $F(x) > 0$.
- For $x > 2$, choose a test point, say $x = 3$: $$F(3) = -3(3) + 6 = -3$$ Therefore, $F(x) < 0$.
At $x = 2$, $F(x) = 0$.
The sign of the functions are as follows: i) $F(x) = x + 5$ is negative for $x < -5$, zero at $x = -5$, and positive for $x > -5$. ii) $F(x) = -3x + 6$ is positive for $x < 2$, zero at $x = 2$, and negative for $x > 2$.