question_answer

Let \[f(x)={{\left( x(x-2) \right)}^{2}}\], \[x\in R\]. Which one of the following is correct?

A) \[f\] has two maxima and one minima

B) \[f\] has only one point of inflection

C) \[f\] increases in the intervals \[(0,1)\cup (2,\infty )\] and decreases in \[(-\infty ,\,0)\cup (1,2)\]

D) \[f\] decreases in the interval \[(0,1)\,\cup \,(2,\infty )\] and increases in the interval \[(-\infty ,0)\,\cup \,(1,2)\].