Question

How do you find the range of `f(x) = x^3 - 3x + 2`?

Answer 1

Since the grade of the function is odd (3), there is no absolute maximum or minimum.

Explanation:

If you let `x` grow, `f(x)` will grow as well, without limit:
Or, in "the language":
`lim_(x->oo) f(x)=oo`
The other way (down) works as well:
`lim_(x->-oo) f(x)=-oo`

There are two local extremes though, which you can find by setting the derivative to zero:
`f'(x)=3x^2-3=0->3x^2=3->x^2=1->`
`x=1or x=-1`
Substituting in `f(x)` you get `(-1,4)and(1,0)`
graph{x^3-3x+2 [-13.7, 14.78, -4.39, 9.85]}