Let y=f(x)=x3+5x23x+1.

(1) Find f(x).

(2) Find the critical points of f(x), that is, find the zeros of f(x).

(3) Find the interval where f(x) is increasing or decreasing.

(4) Find the local minimum and maximum of f(x)

Please, please, please show all of your work so I can actually learn how to solve problems like this.

Thank you!