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Ex 6.5,1 - Chapter 6 Class 12 Application of Derivatives - Part 22

Ex 6.5,1 - Chapter 6 Class 12 Application of Derivatives - Part 23
Ex 6.5,1 - Chapter 6 Class 12 Application of Derivatives - Part 24 Ex 6.5,1 - Chapter 6 Class 12 Application of Derivatives - Part 25

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Ex 6.5,1 (Method 1) Find the maximum and minimum values, if any, of the following functions given by (iv) f(π‘₯) = π‘₯3 + 1f(π‘₯)=π‘₯^3+1 Finding f’(x) f’(π‘₯)=𝑑(π‘₯^3 + 1)/𝑑π‘₯ =3π‘₯^2 Putting f’(𝒙)=𝟎 3π‘₯^2=0 π‘₯^2=0 π‘₯=0 Therefore by first derivate test, the point π‘₯=0 is neither a point of local maxima nor a point of local Minima Hence 𝒙=𝟎 is point of inflexion Hence, there is no minimum or maximum value Ex 6.5, 1 (Method 2) Find the maximum and minimum values, if any, of the following functions given by (iv) f(π‘₯) = π‘₯3 + 1 π‘₯=0 Finding f’’(x) f’(x) = 3x2 f’’(x) = 6x Finding f’’(x) at x = 0 f’’(0) = 6 Γ— 0 = 0 Since f’’(x) = 0 at x = 0 ∴ The point π‘₯=0 is neither a point of local maxima nor a point of local Minima Hence 𝒙=𝟎 is point of inflexion Hence, there is no minimum or maximum value

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.