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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Last updated at April 16, 2024 by Teachoo
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)