help@askiitians.com

+91-735-322-1155

Integral Calculus> Find the intervals in which f(x)=|x-2|÷x²...

question mark

Find the intervals in which f(x)=|x-2|÷x² is strictly increasing and strictly decreasing

KOMATI UMESH , 11 Years ago

Grade 11

1 Answers

Sher Mohammad

$f(x)=\frac{|x-2|}{x^{2}}$

$f(x)=\frac{x-2}{x^{2}} for x>2$

$f(x)=\frac{2-x}{x^{2}} for x<2$

$f'(x)=\frac{4}{x^{3}}-\frac{1}{x^{2}} {\color{Blue} for x>2 }$

$f'(x)=-\frac{4}{x^{3}}+\frac{1}{x^{2}} {\color{Blue} for x<2 }$

for strictly increasing f'(x)>0

$f'(x)=\frac{4}{x^{3}}-\frac{1}{x^{2}}>0 {\color{Blue} for x>2 }$

$f'(x)=-\frac{4}{x^{3}}+\frac{1}{x^{2}}>0 {\color{Blue} for x<2 }$

$x\varepsilon (0,2)\bigcup (4,\varpi )$

for strictly increasing f'(x)<0

$f'(x)=-\frac{4}{x^{3}}+\frac{1}{x^{2}}<0 {\color{Blue} for x<2 }$

$f'(x)=\frac{4}{x^{3}}-\frac{1}{x^{2}}<0 {\color{Blue} for x>2 }$

$x\varepsilon (-\varpi,0)\bigcup (2,4 )$

Sher Mohammad

B.Tech IIT Delhi.

Last Activity: 11 Years ago

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

The area of a square field is 640000cm².what is its area in hectares

integral calculus

1 Answer Available

Last Activity: 3 Years ago

Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request

integral calculus

1 Answer Available

Last Activity: 3 Years ago

Using laplace transform, solve d²y/dt²+ dy/dt = t² +2t given that y=4 and y’=-2 and t=0

integral calculus

1 Answer Available

Last Activity: 3 Years ago

If 4th term of an A.p is zero, show that the 8th term is double the 6th term

integral calculus

1 Answer Available

Last Activity: 3 Years ago

View all Questions