Ex 6.5,10 - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at April 15, 2021 by Teachoo

Ex 6.5, 10 - Find max value of 2x3 - 24 x + 107 in [1, 3]

Ex 6.5,10 - Chapter 6 Class 12 Application of Derivatives - Part 2

Ex 6.5,10 - Chapter 6 Class 12 Application of Derivatives - Part 3

Ex 6.5,10 - Chapter 6 Class 12 Application of Derivatives - Part 4

Transcript

Ex 6.5, 10 Find the maximum value of 2𝑥3 – 24𝑥 + 107 in the interval [1, 3]. Find the maximum value of the same function in [–3, –1]. Let f(𝑥)=2𝑥^3−24𝑥+107 Finding f’(𝑥) f’(𝑥)=𝑑(2𝑥^3 − 24𝑥 + 107)/𝑑𝑥 = 2 × 3𝑥^2−24 = 6𝑥^2−24 = 6 (𝑥^2−4" " ) Putting f(𝑥)=0 6 (𝑥^2−4" " )=0 𝑥^2−4" = 0 " 𝑥^2=4 𝑥=±√4 𝑥=±2 Thus, 𝑥=2 , – 2 Since x is in interval [1 , 3] 𝑥 = 2 is only Critical point Also, since given the interval 𝑥= ∈ [1 , 3] We calculate f(x) at 𝑥= 1 , 2 & 3 Hence maximum value of f(𝒙)=𝟖𝟗 at 𝒙 = 3 in the interval [1 , 3] For the interval [−𝟑 , −𝟏] 𝑥 = –2 is only Critical Point Also, since given the interval 𝑥= ∈ [−3,−1] We calculate f(x) at 𝑥= –1 , –2 & –3 Hence maximum value of f(𝒙)=𝟏𝟑𝟗 at 𝒙 = –2 in the interval [−3,−1]

Next: Ex 6.5,11 Important →

Made by

Davneet Singh

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.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular