Check sibling questions

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

(A)–1Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  (B) 0

(C) 1Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β  Β (D) 2

Β 

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

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Transcript

Question 23 If x is real, the minimum value of x2 – 8x + 17 is –1 (B) 0 (C) 1 (D) 2 𝑓(π‘₯) =π‘₯^2βˆ’8π‘₯+17 Finding 𝒇^β€² (𝒙) 𝒇^β€² (𝒙)=2π‘₯βˆ’8+0 𝑓^β€² (π‘₯)=2π‘₯βˆ’8 𝑓′(π‘₯)=𝟐(π’™βˆ’πŸ’) Putting f’ (𝒙)=𝟎 2(π‘₯βˆ’4)=0 (π‘₯βˆ’4)=0 𝒙=πŸ’ Thus, x = 4 is the minima Finding Minimum value 𝑓(π‘₯) =π‘₯^2βˆ’8π‘₯+17 Putting π‘₯ =4 f(πŸ’)=4^2βˆ’8(4)+17 =16βˆ’32+17 =33βˆ’32 =𝟏 Hence, minimum value of 𝑓(π‘₯) is 1. So, the correct answer is (C)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.