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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