Check sibling questions

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

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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)

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Davneet Singh

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.