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, 11 Prove that the function f given by f (๐ฅ) = ๐ฅ^2 โ ๐ฅ + 1 is neither strictly increasing nor strictly decreasing on (โ 1, 1). Let f(๐ฅ) = ๐ฅ2 โ ๐ฅ + 1 ๐ฅ โ (โ1 , 1) Finding fโ(๐) fโ(๐ฅ) = 2๐ฅ โ 1 Putting fโ(๐) = 0 2๐ฅ โ 1 = 0 2๐ฅ = 1 ๐ฅ = 1/2 Since ๐ฅ โ (โ1 , 1), So, our number line looks like The point ๐ฅ = 1/2 divide the intervals (โ1 , 1) into two disjoint intervals. i.e. (โ1 , 1/2) & (1/2 , 1) Hence, f(x) is strictly decreasing for ๐ฅ โ (โ1 , 1/2) & f(x) is strictly increasing for ๐ฅ โ (1/2, 1) Hence, f(๐ฅ) is neither decreasing nor increasing on (โ๐ , ๐). Hence Proved
About the Author