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

1 Answer
MeneerNask
Jul 7, 2015

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]}

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