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Example 17 - Chapter 6 Class 12 Application of Derivatives
Last updated at August 8, 2026 by Teachoo
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Chapter 6 Class 12 Application of Derivatives
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Example 17 (Method 1) Find all points of local maxima and local minima of the function f given by š (š„)=š„3 ā 3š„ + 3.Finding maximum & minimum value of š(š„)=š„3 ā 3š„+3 Minimum value š(1)=(1)3 ā3(1)+3= 1 ā 3 + 3 = 1 Maximum value š(ā1)=(ā1)3 ā3(ā1)+3= ā1 +3 + 3 = 5 Example 17 (Method 2) Find all points of local maxima and local minima of the function f given by š (š„) = š„3 ā 3š„ + 3. š(š„)=š„3 ā 3š„+3 Finding š^ā² (š) šā²(š„)= 3š„^2 ā 3+0 šā²(š„)= 3(š„^2ā1) Putting šā²(š)= 0 3(š„^2ā1)=0 š„^2ā1=0 (š„ā1)(š„+1)=0 So, x = 1 & x = ā1 Finding šā²ā²(š) š^ā² (š„)=3(š„^2ā1) š^ā²ā² (š„)=3 š(š„^2 ā 1)/šš„ š^ā²ā² (š„)=3(2š„ā0) š^ā²ā² (š„)=6š„ Putting š=āš š^ā²ā² (š„) = 6(ā1) <0 š„ = ā1 is point of local maxima Putting š=š š^ā²ā² (š„) = 6(1) >0 š„ = 1 is point of local minima Finding maximum & minimum value of š(š„)=š„3 ā 3š„+3 Minimum value at x = 1 š(1)=(1)3 ā3(1)+3= 1 ā 3 + 3 = 1 Maximum value at x = ā1 š(ā1)=(ā1)3 ā3(ā1)+3= ā1 + 3 + 3 = 5
