
Last updated at April 14, 2021 by Teachoo
Transcript
Ex 6.2, 18 Prove that the function given by f (๐ฅ) = ๐ฅ3 โ 3๐ฅ2 + 3๐ฅ โ 100 is increasing in R. We need to show f(๐ฅ) is strictly increasing on R i.e. we need to show fโ(๐) > 0 Finding fโ(๐) fโ(๐ฅ)= 3x2 โ 6x + 3 โ 0 = 3(๐ฅ2โ2๐ฅ+1) = 3((๐ฅ)2+(1)2โ2(๐ฅ)(1)) = 3(๐ฅโ1)2 Since Square of any number is always positive (๐ฅโ1)2 > 0 3(๐ฅโ1)2>0 fโ(๐) > 0 Hence, fโ(๐ฅ) > 0 for all values of ๐ฅ โด f(๐ฅ) is strictly increasing on R
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