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


Transcript

Example 17 (Method 1) Find all points of local maxima and local minima of the function f given by 𝑓 (𝑥)=𝑥3 – 3𝑥 + 3.Finding maximum & minimum value of 𝑓(𝑥)=𝑥3 – 3𝑥+3 Minimum value 𝑓(1)=(1)3 –3(1)+3= 1 – 3 + 3 = 1 Maximum value 𝑓(−1)=(−1)3 –3(−1)+3= –1 +3 + 3 = 5 Example 17 (Method 2) Find all points of local maxima and local minima of the function f given by 𝑓 (𝑥) = 𝑥3 – 3𝑥 + 3. 𝑓(𝑥)=𝑥3 – 3𝑥+3 Finding 𝒇^′ (𝒙) 𝑓′(𝑥)= 3𝑥^2 – 3+0 𝑓′(𝑥)= 3(𝑥^2−1) Putting 𝒇′(𝒙)= 0 3(𝑥^2−1)=0 𝑥^2−1=0 (𝑥−1)(𝑥+1)=0 So, x = 1 & x = −1 Finding 𝒇′′(𝒙) 𝑓^′ (𝑥)=3(𝑥^2−1) 𝑓^′′ (𝑥)=3 𝑑(𝑥^2 − 1)/𝑑𝑥 𝑓^′′ (𝑥)=3(2𝑥−0) 𝑓^′′ (𝑥)=6𝑥 Putting 𝒙=−𝟏 𝑓^′′ (𝑥) = 6(−1) <0 𝑥 = –1 is point of local maxima Putting 𝒙=𝟏 𝑓^′′ (𝑥) = 6(1) >0 𝑥 = 1 is point of local minima Finding maximum & minimum value of 𝑓(𝑥)=𝑥3 – 3𝑥+3 Minimum value at x = 1 𝑓(1)=(1)3 –3(1)+3= 1 – 3 + 3 = 1 Maximum value at x = −1 𝑓(−1)=(−1)3 –3(−1)+3= –1 + 3 + 3 = 5

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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.