Question

How do you find the critical numbers for `f(x)= x^3 + x^2 + x` to determine the maximum and minimum?

Answer 1

It doesn't have any.

Explanation:

The critical values for a function are x-values where `f'(x)=0`.

Differentiating the function gives:
`f'(x)=3x^2+2x+1`

You can either use the quadratic formula or your graphing calculator to find the zeros of this function. In the end, you'll get the fact that `f'(x)` is never equal to zero.

Because of this, `f(x)` has no critical values, and no minimum or maximum.