The function f (x) = 2x 3 – 3x 2 – 12x + 4, has

(A) two points of local maximum

(B) two points of local minimum

(C) one maxima and one minima

(D) no maxima or minima

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  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Question 25 The function f (x) = 2x3 โ€“ 3x2 โ€“ 12x + 4, has two points of local maximum (B) two points of local minimum (C) one maxima and one minima (D) no maxima or minima f (๐‘ฅ) = 2๐‘ฅ3 โ€“ 3๐‘ฅ2 โ€“ 12๐‘ฅ + 4 Finding fโ€™ (๐’™) fโ€™ (๐’™) = 6๐‘ฅ2 โ€“ 6๐‘ฅ โ€“ 12 = 6 (๐‘ฅ"2 โ€“" ๐‘ฅ" โ€“ 2" ) = 6 (๐‘ฅ"2 โ€“ 2" ๐‘ฅ "+ " ๐‘ฅ"โ€“ 2 " ) = 6 (๐‘ฅ(๐‘ฅ" โ€“ 2" )+1(๐‘ฅ "โ€“ 2" )) = 6 (๐’™" + " ๐Ÿ) (๐’™ "โ€“" ๐Ÿ) Putting fโ€™ (๐’™) = 0 6 (๐‘ฅ+1) (๐‘ฅโˆ’2) = 0 โˆด ๐’™ = โˆ’1, 2 For maxima or minima Finding fโ€ (๐’™) fโ€ (๐’™) = 12๐‘ฅ โˆ’ 6 For ๐’™ = โˆ’1 fโ€ (โˆ’1) = 12 (โˆ’1) โˆ’6 = โˆ’12 โˆ’ 6 = โˆ’18 < 0 โˆด f has local maxima at x = โˆ’1 For ๐’™ = 2 fโ€ (2) = 12 (2) โˆ’6 = 24 โˆ’ 6 = 18 > 0 โˆด f has local minima at x = 2 Hence, ๐‘“ has one maxima and one minima. So, the correct answer is (C)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.