Ex 6.3, 1 (iv) - Chapter 6 Class 12 Application of Derivatives

Last updated at April 16, 2024 by Teachoo

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Ex 6.3,1 (Method 1) Find the maximum and minimum values, if any, of the following functions given by (iv) f(𝑥) = 𝑥3 + 1f(𝑥)=𝑥^3+1 Finding f’(x) f’(𝑥)=𝑑(𝑥^3 + 1)/𝑑𝑥 =3𝑥^2 Putting f’(𝒙)=𝟎 3𝑥^2=0 𝑥^2=0 𝑥=0 Therefore by first derivate test, the point 𝑥=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 6.3, 1 (Method 2) Find the maximum and minimum values, if any, of the following functions given by (iv) f(𝑥) = 𝑥3 + 1f(𝑥)=𝑥^3+1 Finding f’(x) f’(𝑥)=𝑑(𝑥^3+1)/𝑑𝑥 =3𝑥^2 Putting f’(𝒙)=𝟎 3𝑥^2=0 𝑥^2=0 𝑥=0 Finding f’’(x) f’(x) = 3x2 f’’(x) = 6x Finding f’’(x) at x = 0 f’’(0) = 6 × 0 = 0 Since f’’(x) = 0 at x = 0 ∴ The point 𝑥=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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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