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2015-08-03T15:09:12+05:30

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F(x) = 3 x⁴ + 4x³ - 12 x² + 12
find derivative:
      f '(x) = 12 x³ + 12 x² - 24 x = 0      =>
                 x = 0  or  x² + x - 2 = 0
                    =>  (x +2) (x -1) = 0
   So local maximum of minimum occur at x = -2, 0, 1.

Find the second derivative.
f ' '(x) = 36 x² + 24 x - 24 = 12 (3x² + 2 x - 2)

f ' '(-2) = 72   ,   f ' '(0) =   -24 ,        f ' '(1) = 36

So there is a local minimum at  x  = -2,  a local maximum  at x = 0  and a local minimum at  x = 1.  Local minimum if second derivative is positive.  local maximum when second derivative is negative.

f(x) = 3x⁴ + 4x³ -12 x² + 12
  f(-3) = 39  ,   f(-2) = -30 ,   f(-1) = -1 ,   f(0) = 12     ,    f(1) = 7  ,  f(2) = 44

1 5 1
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