Slide1.JPG

Slide2.JPG

This video is only available for Teachoo black users

  Slide3.JPG Slide4.JPG Slide5.JPG

This video is only available for Teachoo black users

  Slide6.JPG Slide7.JPG Slide8.JPG

 

This video is only available for Teachoo black users

This video is only available for Teachoo black users

This video is only available for Teachoo black users

This video is only available for Teachoo black users

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Ex 6.3, 1 (Method 1) Find the maximum and minimum values, if any, of the following functions given by (i) f (𝑥) = (2𝑥 – 1)^2 + 3 Square of number cant be negative It can be 0 or greater than 0 𝑓(𝑥)=(2𝑥−1)^2+3 Hence, Minimum value of (2𝑥−1)^2 = 0 Minimum value of (2𝑥−1^2 )+3 = 0 + 3 = 3 Also, there is no maximum value of 𝑥 ∴ There is no maximum value of f(x) Ex 6.3, 1 (Method 2) Find the maximum and minimum values, if any, of the following functions given by (i) f (𝑥) = (2𝑥 – 1)^2+3Finding f’(x) f(𝑥)=(2𝑥−1)^2+3 f’(𝑥)= 2(2𝑥−1) Putting f’(𝒙)=𝟎 2(2𝑥−1)=0 2𝑥 – 1 = 0 2𝑥 = 1 𝒙 = 𝟏/𝟐 Thus, x = 1/2 is the minima Finding minimum value f(𝑥)=(2𝑥−1)^2+3 Putting 𝑥 = 1/2 f(1/2)=(2 × 1/2−1)^2+3= (1−1)^2+3= 3 ∴ Minimum value = 3 There is no maximum value Ex 6.3, 1 (Method 3) Find the maximum and minimum values, if any, of the following functions given by (i) 𝑓 (𝑥)= (2𝑥 – 1)^2 + 3Double Derivative Test f(𝑥)=(2𝑥−1)^2+3 Finding f’(𝒙) f’(𝑥)=2(2𝑥−1)^(2−1) = 2(2𝑥−1) Putting f’(𝒙)=𝟎 2(2𝑥−1)=0 (2𝑥−1)=0 2𝑥 = 0 + 1 𝒙 = 𝟏/𝟐 Finding f’’(𝒙) f’(𝑥)=2(2𝑥−1) f’(𝑥) = 4𝑥 – 2 f’’(𝑥)= 4 f’’ (𝟏/𝟐) = 4 Since f’’ (𝟏/𝟐) > 0 , 𝑥 = 1/2 is point of local minima Putting 𝑥 = 1/2 , we can calculate minimum value f(𝑥) = (2𝑥−1)^2+3 f(1/2)= (2(1/2)−1)^2+3= (1−1)^2+3= 3 Hence, Minimum value = 3 There is no Maximum value

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.