![Ex 6.2,18 - Chapter 6 Class 12 Application of Derivatives - Part 2](https://d1avenlh0i1xmr.cloudfront.net/ea14f713-127d-42cc-b061-5e05b2d6fb37/slide32.jpg)
Ex 6.2
Last updated at April 16, 2024 by Teachoo
Ex 6.2, 18 Prove that the function given by f (đĽ) = đĽ3 â 3đĽ2 + 3đĽ â 100 is increasing in R. We need to show f(đĽ) is strictly increasing on R i.e. we need to show fâ(đ) > 0 Finding fâ(đ) fâ(đĽ)= 3x2 â 6x + 3 â 0 = 3(đĽ2â2đĽ+1) = 3((đĽ)2+(1)2â2(đĽ)(1)) = 3(đĽâ1)2 Since Square of any number is always positive (đĽâ1)2 > 0 3(đĽâ1)2>0 fâ(đ) > 0 Hence, fâ(đĽ) > 0 for all values of đĽ â´ f(đĽ) is strictly increasing on R