Question 25
The function f (x) = 2x3 β 3x2 β 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 β 3π₯2 β 12π₯ + 4
Finding fβ (π)
fβ (π) = 6π₯2 β 6π₯ β 12
= 6 (π₯"2 β" π₯" β 2" )
= 6 (π₯"2 β 2" π₯ "+ " π₯"β 2 " )
= 6 (π₯(π₯" β 2" )+1(π₯ "β 2" ))
= 6 (π" + " π) (π "β" π)
Putting fβ (π) = 0
6 (π₯+1) (π₯β2) = 0
β΄ π = β1, 2
For maxima or minima
Finding fβ (π)
fβ (π) = 12π₯ β 6
For π = β1
fβ (β1) = 12 (β1) β6
= β12 β 6
= β18
< 0
β΄ f has local maxima at x = β1
For π = 2
fβ (2) = 12 (2) β6
= 24 β 6
= 18
> 0
β΄ f has local minima at x = 2
Hence, π has one maxima and one minima.
So, the correct answer is (C)

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.

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