Question

The function $\frac{|x-1|}{x^2}$ is monotonically decreasing at the point

• A. $x=3$
• B. $x=2$
• C. $x=1$
• D. none of these

Answer 1

The correct option is A $x=3$

$f\left(x\right)=\frac{|x-1|}{x^2}f\prime \left(x\right)=\frac{2x|x-1|-\frac{|x-1|}{(x-1)}\times x^2}{x^4}f\prime \left(x\right)=02x|x-1|=\frac{|x-1|}{(x-1)}\times x^{2}2x(X-1)=x^{2}x(x-2)=0x=0x=2f\left(3\right)<f\left(2\right)$