Question 12
The function f (x) = 2x3 â 3x2 â 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 (đĽ) = 2đĽ3 â 3đĽ2 â 12đĽ + 4
Finding fâ (đ)
fâ (đ) = 6đĽ2 â 6đĽ â 12
= 6 (đĽ"2 â" đĽ" â 2" )
= 6 (đĽ"2 â 2" đĽ "+ " đĽ"â 2 " )
= 6 (đĽ(đĽ" â 2" )+1(đĽ "â 2" ))
= 6 (đ" + " đ) (đ "â" đ)
Putting fâ (đ) = 0
6 (đĽ+1) (đĽâ2) = 0
â´ đ = â1, 2
For maxima or minima
Finding fâ (đ)
fâ (đ) = 12đĽ â 6
For đ = â1
fâ (â1) = 12 (â1) â6
= â12 â 6
= â18
< 0
â´ f has local maxima at x = â1
For đ = 2
fâ (2) = 12 (2) â6
= 24 â 6
= 18
> 0
â´ f has local minima at x = 2
Hence, đ 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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