Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12


Last updated at Jan. 7, 2020 by Teachoo
Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12
Transcript
Ex 6.2,19 The interval in which ๐ฆ = ๐ฅ2 ๐^(โ๐ฅ) is increasing is (A) (โ โ, โ) (B) (โ 2, 0) (C) (2, โ) (D) (0, 2) Let f(๐ฅ) = ๐ฅ^2 ๐^(โ๐ฅ) Finding fโ(๐) fโ(๐ฅ) = (๐ฅ^2 ๐^(โ๐ฅ) )โฒ fโ(๐ฅ) = (๐ฅ2)โฒ e โ๐ฅ + (๐^(โ๐ฅ) )โ (๐ฅ2) fโ(๐ฅ) = (2๐ฅ) e โ๐ฅ + (ใโ๐ใ^(โ๐ฅ) ) (๐ฅ2) fโ(๐ฅ) = 2๐ฅ e-๐ฅ โ e-๐ฅ ๐ฅ2 fโ(๐ฅ) = ๐ฅ e โ๐ฅ (2โ๐ฅ) Putting fโ(๐)=๐ ๐ฅ e-๐ฅ (2โ๐ฅ) = 0 ๐ฅ (2โ๐ฅ) = 0 So, ๐ฅ=0 & ๐ฅ = 2 Plotting points on real line The points ๐ฅ = 0 & 2 divide the real line into 3 disjoint intervals i.e (โโ , 0) , (0 , 2) & (2 , โ) (As e โ๐ฅ is always positive for all ๐ฅ โ R) Hence, f(๐ฅ) is strictly increasing on (0 , 2) Therefore, correct answer is (๐)
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