`f(x) = x^3 - (3/2)x^2, [-1,2]` Find the absolute extrema of the function on the closed interval.

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Chapter 3, 3.1 - Problem 21 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: `f(x)=x^3-(3/2)x^2,[-1,2]`

First find the critical x value(s) of the function. To find the critical x value(s), set the derivative equal to zero and solve for the x value(s).





Plug the critical x value(s) and the endpoints of the closed interval into the original f(x) function.






Examine the f(x) values.

The absolute maximum is at the point (2, 2).

The absolute minimum is at the point `(-1,-5/2).`


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