The absolute maximum and absolute minimum of the function f(x) = x^3 - x^2 + x – 3 in the domain [-3, 3] has to be found.
The x value of the function where the critical points lie is the solution of the equation f'(x) = 0
f'(x) = 3x^2 - 2x + 1
3x^2 - 2x + 1 = 0
The equation obtained does not have any real solutions.
In the domain [-3, 3] the minimum value lies at x = -3 and the maximum value at x = 3.
The function f(x) = x^3 - x^2 + x – 3 has a minimum at x = -3 and a maximum at x = 3