Question

Is `f(x)=(x-3)^3+3x^2-2x` increasing or decreasing at `x=0`?

Answer 1

Hence, `f` is increasing at `x=0.`

Explanation:

We use the criteria `f'(a)>0` `rArr` `f` is `uarr` at `a.`
`f'(a)<0` `rArr` `f` is `darr` at `a`.

Now, `f(x)=(x-3)^3+3x^2-2x. rArr f'(x)=3(x-3)^2+6x-2 rArr f'(0)=3(-3)^2-2=25>0`

Hence, `f` is increasing at `x=0.`