Question

Let $f\left(x\right)=2x^2-ln|x|,x\ne 0,thenf\left(x\right)$ is

• A. Monotonically increasing in $(-\frac{1}{2},0)\cup (\frac{1}{2},\infty )$
• B. Monotonically decreasing in $(-\frac{1}{2},0)\cup (\frac{1}{2},\infty )$
• C. Monotonically increasing in $(-\infty ,-\frac{1}{2})\cup (0,\frac{1}{2})$
• D. Monotonically decreasing in $(-\infty ,-\frac{1}{2})\cup (0,\frac{1}{2})$

Answer 1

Answer: (A), (D)

The correct options are
A Monotonically increasing in $(-\frac{1}{2},0)\cup (\frac{1}{2},\infty )$
D Monotonically decreasing in $(-\infty ,-\frac{1}{2})\cup (0,\frac{1}{2})$

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

f is increasing $\Rightarrow f^1\left(x\right)>0$
f is decreasing $\Rightarrow f^1\left(x\right)>0$