Function f(x) = (\frac{|x–1|}{x^{2}}) is monotonic decreasin... | MATH - INCREASING AND DECREASING FUNCTION | SolveeIt

Function f(x) = $\frac{|x–1|}{x^{2}}$ is monotonic decreasing in –

(– , )

(0, 1)

(2, )

(– , 1) Č (2, )

Answer

(– , 1) Č (2, )

Explanation

f(x) = $\left\{ \begin{matrix} \frac{1–x}{x^{2}},x < 1 \\ \frac{x–1}{x^{2}},x > 1 \end{matrix} \right.\$

f ¢(x) = $\left\{ \begin{matrix} \frac{1}{x^{2}}–\frac{2}{x^{3}},x < 1 \\ \frac{2}{x^{3}}–\frac{1}{x^{2}},x > 1 \end{matrix} \right.\$

f(x) is decreasing Ž f ¢(x) < 0

Ž $\left\{ \begin{matrix} \frac{x–2}{x^{3}} < 0,x < 1 \\ \frac{2–x}{x^{3}} < 0,x > 1 \end{matrix} \right.\$ Ž x < 1, x > 2

Question: Function f(x) = \(\frac{|x–1|}{x^{2}}\) is monotonic decreasing in –...