# What are the absolute extrema of # f(x)= x^3 -3x+1 in [0,3]#?

##### 1 Answer

#### Answer:

Absolute minimum of

#### Explanation:

There are two candidates for the absolute extrema of an interval. They are the endpoints of the interval (here,

The critical values can be found by finding the function's derivative and finding for which values of

We can use the power rule to find that the derivative of

The critical values are when

To determine which is which, plug them all into the original function.

From here we can see that there is an absolute minimum of

Check the function's graph:

graph{x^3-3x+1 [-0.1, 3.1, -5, 20]}