Misc 10 - Chapter 6 Class 12 Application of Derivatives
Last updated at August 2, 2026 by Teachoo
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Chapter 6 Class 12 Application of Derivatives
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Misc 10 Find the points at which the function f given by f (š„) = (š„ā2)^4 (š„+1)^3 has (i) local maxima (ii) local minima (iii) point of inflexionf(š„)= (š„ā2)^4 (š„+1)3 Finding fā(š) fā(š„) = (š ((š„ ā 2)^4 (š„ + 1)^3 ))/šš„ = ć((š„ā2)^4 )^ā² (š„+1)ć^3+((š„+1)^3 )^ā² (š„ā2)^4 = 4(š„ā2)^3 (š„+1)^3+3(š„+1)^2 (š„ā2)^4 = (š„ā2)^3 (š„+1)^2 [4(š„+1)+3(š„ā2)] = (š„ā2)^3 (š„+1)^2 [4š„+4+3š„ā6] = (šāš)^š (š+š)^š [ššāš] Putting fā(š)=š (š„ā2)^3 (š„+1)^2 (7š„ā2)=0 Hence, š„=2 & š„=ā1 & š„=2/7 = 0.28 (š„ā2)^3 = 0 š„ ā 2 = 0 š=š (š„+1)^2=0 (š„+1)=0 š = ā1 7š„ ā 2 = 0 7š„ = 2 š = š/š Thus, š„=āš is a point of Inflexion š„=š/š is point of maxima š„=š is point of minima
