F(x)=x^3+x^2-x-1 identify its relative maximum and minimum

local minimum at  x = 1/3

local maximum at x = -1

Step-by-step explanation:

F(x)=x^3+x^2-x-1 identify its relative maximum and minimum

cubic function

find  dF(x)/dx  =  3xx + 2x - 1

3xx + 2x - 1 = 0

3xx + 3x - x - 1 = 0

3x(x + 1) - (x + 1) = 0

(3x - 1)(x + 1) = 0

local extrema at  (3x - 1) = 0  and (x + 1) = 0

x = 1/3  and x = -1

check 2nd derivative

ddF(x)/ddx =  6x + 2

ddF(1/3)/ddx  =  6*(1/3) + 2 = 4  > 0

local minimum at  x = 1/3

ddF(-1)/ddx = 6*(-1) + 2 = -4 < 0

local maximum at x = -1