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Ex 6.5
Ex 6.5, 1 (ii)
Ex 6.5, 1 (iii) Important
Ex 6.5, 1 (iv)
Ex 6.5, 2 (i)
Ex 6.5, 2 (ii) Important
Ex 6.5, 2 (iii)
Ex 6.5, 2 (iv) Important
Ex 6.5, 2 (v) Important
Ex 6.5, 3 (i)
Ex 6.5, 3 (ii)
Ex 6.5, 3 (iii) You are here
Ex 6.5, 3 (iv) Important
Ex 6.5, 3 (v)
Ex 6.5, 3 (vi)
Ex 6.5, 3 (vii) Important
Ex 6.5, 3 (viii)
Ex 6.5, 4 (i)
Ex 6.5, 4 (ii) Important
Ex 6.5, 4 (iii)
Ex 6.5, 5 (i)
Ex 6.5, 5 (ii)
Ex 6.5, 5 (iii) Important
Ex 6.5, 5 (iv)
Ex 6.5,6
Ex 6.5,7 Important
Ex 6.5,8
Ex 6.5,9 Important
Ex 6.5,10
Ex 6.5,11 Important
Ex 6.5,12 Important
Ex 6.5,13
Ex 6.5,14 Important
Ex 6.5,15 Important
Ex 6.5,16
Ex 6.5,17
Ex 6.5,18 Important
Ex 6.5,19 Important
Ex 6.5, 20 Important
Ex 6.5,21
Ex 6.5,22 Important
Ex 6.5,23 Important
Ex 6.5,24 Important
Ex 6.5,25 Important
Ex 6.5, 26 Important
Ex 6.5, 27 (MCQ)
Ex 6.5,28 (MCQ) Important
Ex 6.5,29 (MCQ)
Last updated at March 30, 2023 by Teachoo
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)=sin𝑥+cos𝑥, 0<𝑥<𝜋/2 ℎ(𝑥)=sin𝑥+cos𝑥, 0<𝑥<𝜋/2 Finding 𝒉′(𝒙) ℎ′(𝑥)=𝑑(sin𝑥 + cos𝑥" " )/𝑑𝑥 ℎ^′ (𝑥)=cos𝑥−sin𝑥 Putting 𝒉′(𝒙)=𝟎 cos𝑥−𝑠𝑖𝑛𝑥=0 cos〖𝑥=𝑠𝑖𝑛 𝑥〗 1 = sin𝑥/cos𝑥 1 = tan 𝑥 tan 𝑥=1 ∴ 𝑥=45°= 𝜋/4 Finding h’’(𝒙) h’(𝑥)=cos𝑥−sin𝑥 h’’(𝑥)=−sin𝑥−cos𝑥 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