If x is real, the minimum value of x 2 – 8x + 17 is

(A)–1                                (B) 0

(C) 1                                 (D) 2

 

This question is similar to Ex 6.5, 1 (i) - Chapter 6 Class 12 - Application of Derivatives

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

Transcript

Question 23 If x is real, the minimum value of x2 โ€“ 8x + 17 is โ€“1 (B) 0 (C) 1 (D) 2 ๐‘“(๐‘ฅ) =๐‘ฅ^2โˆ’8๐‘ฅ+17 Finding ๐’‡^โ€ฒ (๐’™) ๐’‡^โ€ฒ (๐’™)=2๐‘ฅโˆ’8+0 ๐‘“^โ€ฒ (๐‘ฅ)=2๐‘ฅโˆ’8 ๐‘“โ€ฒ(๐‘ฅ)=๐Ÿ(๐’™โˆ’๐Ÿ’) Putting fโ€™ (๐’™)=๐ŸŽ 2(๐‘ฅโˆ’4)=0 (๐‘ฅโˆ’4)=0 ๐’™=๐Ÿ’ Thus, x = 4 is the minima Finding Minimum value ๐‘“(๐‘ฅ) =๐‘ฅ^2โˆ’8๐‘ฅ+17 Putting ๐‘ฅ =4 f(๐Ÿ’)=4^2โˆ’8(4)+17 =16โˆ’32+17 =33โˆ’32 =๐Ÿ Hence, minimum value of ๐‘“(๐‘ฅ) is 1. 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.