Check sibling questions

Ex 6.5, 3 (iii) - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at March 30, 2023 by

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

Ex 6.5,3 - Chapter 6 Class 12 Application of Derivatives - Part 7
Ex 6.5,3 - Chapter 6 Class 12 Application of Derivatives - Part 8 Ex 6.5,3 - Chapter 6 Class 12 Application of Derivatives - Part 9

Get live Maths 1-on-1 Classs - Class 6 to 12

Book 30 minute class for ₹ 499 ₹ 299

Transcript

Ex 6.5, 3 Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (iii) ℎ(𝑥)=sin⁡𝑥+cos⁡𝑥, 0<𝑥<𝜋/2 ℎ(𝑥)=sin⁡𝑥+cos⁡𝑥, 0<𝑥<𝜋/2 Finding 𝒉′(𝒙) ℎ′(𝑥)=𝑑(sin⁡𝑥 + cos⁡𝑥" " )/𝑑𝑥 ℎ^′ (𝑥)=cos⁡𝑥−sin⁡𝑥 Putting 𝒉′(𝒙)=𝟎 cos⁡𝑥−𝑠𝑖𝑛𝑥=0 cos⁡〖𝑥=𝑠𝑖𝑛 𝑥〗 1 = sin⁡𝑥/cos⁡𝑥 1 = tan 𝑥 tan 𝑥=1 ∴ 𝑥=45°= 𝜋/4 Finding h’’(𝒙) h’(𝑥)=cos⁡𝑥−sin⁡𝑥 h’’(𝑥)=−sin⁡𝑥−cos⁡𝑥 Putting 𝒙=𝝅/𝟒 h’’(π/4)=−sin(π/4)−𝑐𝑜𝑠(π/4) = – 1/√2−1/√2 = (−2)/√2 = – √2 Since h’’(𝑥)<0 when 𝑥=π/4 ∴ 𝑥=π/4 is point of Local Maxima f has Maximum value at 𝒙=𝝅/𝟒 f(𝑥)=𝑠𝑖𝑛𝑥+𝑐𝑜𝑠𝑥 f(π/4)=𝑠𝑖𝑛(π/4)+𝑐𝑜𝑠(π/4) = 1/√2+1/√2 = 2/√2 = √𝟐

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.