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
Example 18 Find the equation of the tangent to the curve y = (๐ฅ โ 7)/((๐ฅ โ 2)(๐ฅ โ 3)) at the point where it cuts the x-axis. Slope of the tangent to the curve is ๐๐ฆ/๐๐ฅ = ((๐ฅ โ 7)^โฒ [(๐ฅ โ 2) (๐ฅ โ 3)]โ (๐ฅ โ 7) [(๐ฅ โ 3) (๐ฅ โ 2)]^โฒ)/((๐ฅ โ 2)^2 (๐ฅ โ 3)^2 ) ๐๐ฆ/๐๐ฅ = (1 ร (๐ฅ โ 2) (๐ฅ โ 3) โ (๐ฅ โ 7)[(๐ฅ โ 3)^โฒ (๐ฅ โ 2) + (๐ฅ โ 3) (๐ฅ โ 2)^โฒ ])/((๐ฅ โ 2)^2 (๐ฅ โ 3)^2 ) ๐๐ฆ/๐๐ฅ = ((1) (๐ฅ โ 2) (๐ฅ โ 3) โ (๐ฅ โ 7)[1 ร (๐ฅ โ 2) + (๐ฅ โ 3) ร 1])/((๐ฅ โ 2)^2 (๐ฅ โ 3)^2 ) ๐๐ฆ/๐๐ฅ = ((๐ฅ โ 2) (๐ฅ โ 3) โ (๐ฅ โ 7)(2๐ฅ โ 5))/((๐ฅ โ 2)^2 (๐ฅ โ 3)^2 ) ๐๐ฆ/๐๐ฅ = ((๐ฅ โ 2) (๐ฅ โ 3) )/((๐ฅ โ 2)^2 (๐ฅ โ 3)^2 )โ(๐ฅ โ 7)(2๐ฅ โ 5)/((๐ฅ โ 2)^2 (๐ฅ โ 3)^2 ) ๐๐ฆ/๐๐ฅ = (1 )/((๐ฅ โ 2) (๐ฅ โ 3) )โ((๐ฅ โ 7))/((๐ฅ โ 2) (๐ฅ โ 3) ) ร ((2๐ฅ โ 5))/((๐ฅ โ 2) (๐ฅ โ 3) ) ๐๐ฆ/๐๐ฅ = (1 )/((๐ฅ โ 2) (๐ฅ โ 3) )โ๐ฆ ร ((2๐ฅ โ 5))/((๐ฅ โ 2) (๐ฅ โ 3) ) ๐๐ฆ/๐๐ฅ = (1 โ ๐ฆ(2๐ฅ โ 5))/((๐ฅ โ 2) (๐ฅ โ 3) ) We need to find equation of tangent at the point where the curve cuts the x axis, y = 0 Hence the equation of the curve is 0 = (๐ฅ โ 7)/(๐ฅ โ 2)(๐ฅ โ 3) โด x = 7 Thus, curve cuts the x โ axis at point (7, 0) At point (7, 0) the slope is ๐๐ฆ/๐๐ฅ = (1 โ ๐ฆ(2๐ฅ โ 5))/((๐ฅ โ 2) (๐ฅ โ 3) ) [๐๐ฆ/๐๐ฅ]_((7, 0) ) = (1 โ 0[2(7)โ5])/((7 โ 2) (7 โ 3) ) = 1/(5 ร 4) = 1/20 Now, Equation of the tangent at point (7, 0) with slope 1/20 is ๐ฆ โ๐ฆ_1= ๐ (๐ฅ โ ๐ฅ1) ๐ฆโ0= 1/20 (๐ฅโ7) 20๐ฆ=๐ฅโ7 ๐๐๐โ๐+๐=๐ Now, Equation of the tangent at point (7, 0) with slope 1/20 is ๐ฆ โ๐ฆ_1= ๐ (๐ฅ โ ๐ฅ1) ๐ฆโ0= 1/20 (๐ฅโ7) 20๐ฆ=๐ฅโ7 ๐๐๐โ๐+๐=๐
Examples
Example 2 Not in Syllabus - CBSE Exams 2021
Example 3 Not in Syllabus - CBSE Exams 2021
Example 4 Important Not in Syllabus - CBSE Exams 2021
Example 5 Not in Syllabus - CBSE Exams 2021
Example 6 Not in Syllabus - CBSE Exams 2021
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Example 8 Important
Example 9 Important
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Example 11 Important
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Example 13 Important
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Example 17 Important
Example 18 You are here
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Example 21 Not in Syllabus - CBSE Exams 2021
Example 22 Not in Syllabus - CBSE Exams 2021
Example 23 Not in Syllabus - CBSE Exams 2021
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Example 28 Important
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Example 38 Important
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Example 40 Important
Example 41 Important
Example 42 Important Not in Syllabus - CBSE Exams 2021
Example 43 Important Not in Syllabus - CBSE Exams 2021
Example 44 Important Not in Syllabus - CBSE Exams 2021
Example 45 Important
Example 46 Important
Example 47 Important
Example 48 Important
Example 49 Not in Syllabus - CBSE Exams 2021
Example 50 Important
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