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 6.3, 11 Find the equation of all lines having slope 2 which are tangents to the curve ๐ฆ=1/(๐ฅ โ 3) , ๐ฅโ 3. The Equation of Given Curve is : ๐ฆ=1/(๐ฅ โ 3) We know that Slope of tangent is ๐๐ฆ/๐๐ฅ ๐๐ฆ/๐๐ฅ=๐(1/(๐ฅ โ 3))/๐๐ฅ ๐๐ฆ/๐๐ฅ=๐/๐๐ฅ (๐ฅโ3)^(โ1) ๐๐ฆ/๐๐ฅ=(โ1) (๐ฅโ3)^(โ1โ1) . ๐(๐ฅ โ 3)/๐๐ฅ ๐๐ฆ/๐๐ฅ=โ(๐ฅโ3)^(โ2) ๐๐ฆ/๐๐ฅ=(โ1)/(๐ฅ โ 3)^2 Given that slope = 2 Hence, ๐๐ฆ/๐๐ฅ = 2 โด (โ1)/(๐ฅ โ 3)^2 =2 โ1=2(๐ฅโ3)^2 ใ2(๐ฅโ3)ใ^2=โ1 (๐ฅโ3)^2=(โ1)/( 2) We know that Square of any number is always positive So, (๐ฅโ3)^2>0 โด (๐ฅโ3)^2=(โ1)/( 2) not possible Thus, No tangent to the Curve has Slope 2
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