Prove that function f(x) =`{-2x^(3)+3x^(2)-6x+5,xlt0` `-x^(2)-x+1, xge0` is decreasing for all x.

Explanation

To prove that the function \( f(x) \) is decreasing for all \( x \), we will analyze the derivative of the function in both cases: when \( x < 0 \) and when \( x \geq 0 \).

### Step 1: Define the function
The given function is:
\[
f(x) =
\begin{cases}
-2x^3 + 3x^2 - 6x + 5 & \text{if } x < 0 \\
...