alleryThe function $f(x)=x^2-4x+6$ is decreasing on the interval
A$(2,\infty)$
B$(0,2)$
C$(-\infty,\infty)$
D$(-\infty,2)$
Answer & Solution
Correct answer: D. $(-\infty,2)$
1. $f'(x)=2x-4$.
2. $f'(x)=0$ at $x=2$.
3. For $x<2$, $f'(x)<0$, so $f$ is decreasing on $(-\infty,2)$.
4. For $x>2$, $f'(x)>0$ (increasing), ruling out $(2,\infty)$.
_Source: syllabus Mathematics Ch 6 "Application of Derivatives", p.8_
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