# Over what intervals is # f(x)=(x-1)^2-x^3+x # increasing and decreasing?

##### 1 Answer

#### Explanation:

We will have to differentiate the function:

- If
#f'>0# , then#f# is increasing. - If
#f'<0# , then#f# is decreasing.

First, simplify

#f(x)=x^2-2x+1-x^3+x#

#f(x)=-x^3+x^2-x+1#

Now, find **power rule**.

#f'(x)=-3x^2+2x-1#

In order to analyze when

#-3x^2+2x-1=0#

We see that the polynomial has a negative discriminant, which means the that

The graph of

graph{(x-1)^2-x^3+x [-13.41, 15.07, -6.32, 7.92]}

The graph of

graph{-3x^2+2x-1 [-20.13, 20.42, -12.77, 7.5]}