Ex 6.5

Chapter 6 Class 12 Application of Derivatives
Serial order wise

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### Transcript

Ex 6.5, 3 Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (ii) π(π₯)=π₯3 β3π₯π(π₯)=π₯3 β3π₯ Finding gβ(π) gβ(π₯)=π(π₯^3 β 3π₯)/ππ₯ gβ(π₯)=3π₯^2β3 Putting gβ(π)=π 3π₯^2β3=0 3π₯^2=3 π₯^2=3/3 π₯^2=1 π₯=Β±1 So, x = 1 & x = β1 Finding gββ(π) gβ(π₯)=3π₯^2β3 gββ(π₯)=π(3π₯^2β3)/ππ₯ = 6π₯β0 = 6π₯ Putting π=π in gββ(x) gββ(1)=6(1)= 6 > 0 Thus, gββ(π₯)>0 when π₯=1 β π₯=1 is point of local minima & g(π₯) is minimum at π₯=1 Local minimum value g(π₯)=π₯^3β3π₯ g(1)=(1)^3β3(1) =1β3 =βπ Putting π=βπ in gββ(x) gββ(β1)=6(β1)= β6 < 0 Thus, gββ(π₯)<0 when π₯=β1 β π₯=β1 is point of local maxima & g(π₯) is maximum at π₯=β1 Local minimum value g(π₯)=π₯^3β3π₯ g(β1)=(β1)^3β3(β1) =β1+3 =π