Ex 6.3, 2 - Find slope of tangent y = x-1/x-2, at x = 10 - Ex 6.3

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  1. Chapter 6 Class 12 Application of Derivatives
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Ex 6.3,2 Find the slope of the tangent to the curve 𝑦= 𝑥 − 1﷮𝑥 − 2﷯ , 𝑥≠2 at 𝑥=10 𝑦= 𝑥 − 1﷮𝑥 − 2﷯ 𝑥≠2 We know that Slope of tangent is 𝑑𝑦﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯= 𝑑 𝑥 − 1﷮𝑥 − 2﷯﷯ ﷮𝑑𝑥﷯ 𝑑𝑦﷮𝑑𝑥﷯= 𝑥 − 1﷯﷮′﷯ 𝑥 − 2﷯ − 𝑥 − 2﷯﷮′﷯ 𝑥 − 1﷯﷮ 𝑥 − 2﷯﷮2﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯= 1 𝑥 − 2﷯ −1 𝑥 − 1﷯﷮ 𝑥 − 2﷯﷮2﷯﷯ 𝑑𝑦﷮𝑑𝑥﷯= 𝑥 − 2 − 𝑥 + 1﷮ 𝑥 − 2﷯﷮2﷯﷯ So, 𝑑𝑦﷮𝑑𝑥﷯= − 1﷮ 𝑥 − 2﷯﷮2﷯﷯ Putting 𝑥=10 𝑑𝑦﷮𝑑𝑥﷯﷯﷮𝑥 = 10﷯= − 1﷮ 10 − 2﷯﷮2﷯﷯ = − 1﷮ 8﷮2﷯﷯ = − 1﷮64﷯ Hence Slope of a tangent at 𝑥 = 10 is −𝟏﷮𝟔𝟒﷯

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