Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

Last updated at April 15, 2021 by Teachoo

Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

Transcript

Ex 6.5, 4 Prove that the following functions do not have maxima or minima: (i) π (π₯) = π^π₯Given π (π₯) = π^π₯ Finding maxima or minima πβ²(π₯) = π^π₯ Putting fβ (x) = 0 ππ₯ = 0 This is not possible for any value of x. β΄ f (x) does not have a maxima or minima. Ex 6.5, 4 Prove that the following functions do not have maxima or minima: (ii) g(x) = log xGiven g (x) = log x Finding maxima or minima gβ (x) = 1/π₯ Putting gβ (x) = 0 1/π₯=0 π₯ =1/0 π₯ = β This is not defined for x. So, g (x) does not have a maxima or minima. Ex 6.5, 4 Prove that the following functions do not have maxima or minima: (iii) β(π₯)= π₯^3+π₯^2+π₯+1Given h (x) = x3 + x2 + x + 1 Finding maxima or minima ββ (π₯) = 3π₯^2+2π₯+1 Putting ββ (π₯)= 0 3π₯^2+2π₯+1=0 For ax2 + bx + c = 0 x = (βπ Β± β(π^2 β 4ππ))/2π Here π = 3, b = 2, & c = 1 x = (β 2 Β± β(4 β 4(3)(1)))/6 x = (β 2 Β± β(4 β 12))/6 x = (β2 Β± β(β 8))/6 x = (β 2 Β± 2β(β 2))/6 x = (βπ Β± β(β π))/π Since root has minus sign, x has no real value β΄ h (x) does not have a maxima of minima

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Chapter 6 Class 12 Application of Derivatives

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.