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

Jun 30, 2017

It doesn't have any.

#### Explanation:

The critical values for a function are x-values where $f ' \left(x\right) = 0$.

Differentiating the function gives:
$f ' \left(x\right) = 3 {x}^{2} + 2 x + 1$

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 $f ' \left(x\right)$ is never equal to zero.

Because of this, $f \left(x\right)$ has no critical values, and no minimum or maximum.
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