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Example 39 - Find absolute maximum, minimum values of f(x) - Absolute minima/maxima

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  1. Chapter 6 Class 12 Application of Derivatives
  2. Serial order wise
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Example 39 Find the absolute maximum and minimum values of a function f given by 𝑓 (đ‘„) = 2đ‘„3 – 15đ‘„2 + 36đ‘„ +1 on the interval [1, 5]. fï·đ‘„ï·Ż = 2đ‘„3 – 15đ‘„2 + 36đ‘„ + 1 fâ€™ï·đ‘„ï·Ż=6ï·đ‘„ï·ź2ï·Żâˆ’30đ‘„+36 Putting f â€™ï·đ‘„ï·Ż=0 6đ‘„2 – 30đ‘„ + 36 = 0 6ï·ï·đ‘„ï·ź2ï·Żâˆ’5đ‘„+6ï·Ż=0 ï·ï·đ‘„ï·ź2ï·Żâˆ’5đ‘„+6ï·Ż=0 ï·ï·đ‘„ï·ź2ï·Żâˆ’2đ‘„âˆ’3đ‘„+6ï·Ż=0 đ‘„ï·đ‘„âˆ’2ï·Żâˆ’3ï·đ‘„âˆ’2ï·Ż=0 ï·đ‘„âˆ’2ï·Żï·đ‘„âˆ’3ï·Ż=0 Hence đ‘„ = 2 or đ‘„ = 3 We are given interval ﷐1 , 5ï·Ż Hence calculating fï·đ‘„ï·Ż at đ‘„ = 2, 3, 1, 5 Hence, Absolute maximum value is 56 at 𝒙=𝟓 Absolute minimum value is 24 at 𝒙=𝟏

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