Check sibling questions

Question 25 - NCERT Exemplar - MCQs - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at March 22, 2023 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

Slide99.JPG

Slide100.JPG
Slide101.JPG

This video is only available for Teachoo black users

Subscribe Now

Get live Maths 1-on-1 Classs - Class 6 to 12

Book 30 minute class for β‚Ή 499 β‚Ή 299

Transcript

Question 25 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 (π‘₯) = 2π‘₯3 – 3π‘₯2 – 12π‘₯ + 4 Finding f’ (𝒙) f’ (𝒙) = 6π‘₯2 – 6π‘₯ – 12 = 6 (π‘₯"2 –" π‘₯" – 2" ) = 6 (π‘₯"2 – 2" π‘₯ "+ " π‘₯"– 2 " ) = 6 (π‘₯(π‘₯" – 2" )+1(π‘₯ "– 2" )) = 6 (𝒙" + " 𝟏) (𝒙 "–" 𝟏) Putting f’ (𝒙) = 0 6 (π‘₯+1) (π‘₯βˆ’2) = 0 ∴ 𝒙 = βˆ’1, 2 For maxima or minima Finding f” (𝒙) f” (𝒙) = 12π‘₯ βˆ’ 6 For 𝒙 = βˆ’1 f” (βˆ’1) = 12 (βˆ’1) βˆ’6 = βˆ’12 βˆ’ 6 = βˆ’18 < 0 ∴ f has local maxima at x = βˆ’1 For 𝒙 = 2 f” (2) = 12 (2) βˆ’6 = 24 βˆ’ 6 = 18 > 0 ∴ f has local minima at x = 2 Hence, 𝑓 has one maxima and one minima. So, the correct answer is (C)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.