Find the absolute maximum and absolute minimum of the function  f(x)= (x^3) - (x^2) + x – 3 for `(-3 <= x <= 3)`      

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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

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