Question

What are the critical values, if any, of `f(x)= x^3 - 4x^2 + 11`?

Answer 1

`c=0,8/3`

Explanation:

The critical values are the `x`-values at which the derivative of the function is equal to zero or does not exist.

Find `f'(x)`.

`f'(x)=3x^2-8x`

Set `f'(x)=0`.

`3x^2-8x=0=>x(3x-8)=0`

`x=0,8/3`

These are two critical values.

Since `f'(x)` is never undefined, there are no critical values there.

Thus, the only two are `0,8/3`.

graph{x^3-4x^2+11 [-17.27, 18.77, -3.52, 14.5]}