Answer:
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
