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