Question

The function $f\left(x\right)=x^2(x-2{)}^2$

• A. Decreases on (0, 1) ∪ (2, ∞)
• B. Increase on (-∞, 0) ∪ (1, 2)
• C. Has a local maximum value 0
• D. Has local maximum value 1

Answer 1

The correct option is D

Has local maximum value 1

$f\left(x\right)=x^2(x-2{)}^2$

$f^{\prime }\left(x\right)=2x(x-2{)}^2+2x^2+(x-2)=4x(x-2\left)\right(x-1)$

$f^{\prime }\left(x\right)\ge 0forx\epsilon [0,1]\cup [2,\infty ]f^{\prime }\left(x\right)\le 0forx\epsilon (-\infty ,0)\cup [1,2]$