Ex 6.3,7 - Chapter 6 Class 12 Application of Derivatives

Last updated at June 12, 2023 by Teachoo

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Ex 6.3, 7 Find both the maximum value and the minimum value of 3𝑥4 – 8𝑥3 + 12𝑥2 – 48𝑥 + 25 on the interval [0, 3].Let f(x) = 3𝑥4 – 8𝑥3 + 12𝑥2 – 48𝑥 + 25, where 𝑥 ∈ [0, 3] Finding f’(𝒙) f’(𝑥)=𝑑(3𝑥^4 − 8𝑥^3 + 12𝑥^2 − 48𝑥 + 25)/𝑑𝑥 f’(𝑥)=3 ×4𝑥^3−8 ×3𝑥^2+12 ×2𝑥−48+0 f’(𝑥)=12𝑥^3−24𝑥^2+24𝑥−48 f’(𝑥)=12(𝑥^3−2𝑥^2+2𝑥−4) Putting f’(𝒙)=𝟎 12(𝑥^3−2𝑥^2+2𝑥−4)=0 𝑥^3−2𝑥^2+2𝑥−4=0 𝑥^2 (𝑥−2)+2(𝑥−2)=0 (𝑥^2+2)(𝑥−2)=0 Since 𝑥^2=−2 is not possible Thus 𝑥=2 is only critical point Since are given interval 𝑥 ∈ [0 , 3] Hence , calculating f(𝑥) at 𝑥 = 0 , 2 & 3 Hence, Minimum value of f(𝑥) is –39 at 𝒙 = 2 Maximum value of f(𝑥) is 25 at 𝒙 = 0

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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