Find local max. & min. values of the function f given by f(x)=3x^4+4x^3-12x^2+12

1
by anujRamesh8

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

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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

click on thanks button above please