Question 12 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives

Last updated at Dec. 16, 2024 by

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

The function f (x) = 2x3 – 3x2 – 12x + 4, has - Class 12 MCQ [Teachoo] - NCERT Exemplar - MCQs

part 2 - Question 12 - NCERT Exemplar - MCQs - Serial order wise - Chapter 6 Class 12 Application of Derivatives
part 3 - Question 12 - NCERT Exemplar - MCQs - Serial order wise - Chapter 6 Class 12 Application of Derivatives

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Question 12 The function f (x) = 2x3 – 3x2 – 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 (𝑥) = 2𝑥3 – 3𝑥2 – 12𝑥 + 4 Finding f’ (𝒙) f’ (𝒙) = 6𝑥2 – 6𝑥 – 12 = 6 (𝑥"2 –" 𝑥" – 2" ) = 6 (𝑥"2 – 2" 𝑥 "+ " 𝑥"– 2 " ) = 6 (𝑥(𝑥" – 2" )+1(𝑥 "– 2" )) = 6 (𝒙" + " 𝟏) (𝒙 "–" 𝟏) Putting f’ (𝒙) = 0 6 (𝑥+1) (𝑥−2) = 0 ∴ 𝒙 = −1, 2 For maxima or minima Finding f” (𝒙) f” (𝒙) = 12𝑥 − 6 For 𝒙 = −1 f” (−1) = 12 (−1) −6 = −12 − 6 = −18 < 0 ∴ f has local maxima at x = −1 For 𝒙 = 2 f” (2) = 12 (2) −6 = 24 − 6 = 18 > 0 ∴ f has local minima at x = 2 Hence, 𝑓 has one maxima and one minima. So, the correct answer is (C)

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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 and Computer Science at Teachoo