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




Question 10 If x is real, the minimum value of x2 – 8x + 17 is –1 (B) 0 (C) 1 (D) 2 𝑓(𝑥) =𝑥^2−8𝑥+17 Finding 𝒇^′ (𝒙) 𝒇^′ (𝒙)=2𝑥−8+0 𝑓^′ (𝑥)=2𝑥−8 𝑓′(𝑥)=𝟐(𝒙−𝟒) Putting f’ (𝒙)=𝟎 2(𝑥−4)=0 (𝑥−4)=0 𝒙=𝟒 Thus, x = 4 is the minima Finding Minimum value 𝑓(𝑥) =𝑥^2−8𝑥+17 Putting 𝑥 =4 f(𝟒)=4^2−8(4)+17 =16−32+17 =33−32 =𝟏 Hence, minimum value of 𝑓(𝑥) is 1. So, the correct answer is (C)

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.