How would you graph f(x) given that f(x)=x3? Can i have a detailed explanation o

Question

How would you graph f(x) given that f(x)=x3?
Can i have a detailed explanation of it? Like where the main points are. Thank you very much! How would you graph f(x) given that f(x)=x3?
Can i have a detailed explanation of it? Like where the main points are. Thank you very much!

Explanation / Answer

f(x)=x^3 f '(x)=3x^2=0 when x=0 first derivative f ''(x)=6x=0 when x=0 second derivative f ' (x) >=0 for all x, concavity changes at x=0 (0,0) is the point of inflection using a TI-89 titanium enter f(x) by pressing the yellow diamond and F1 with cursor on y1 press enter now enter f(x) press enter now press F2 than 6 for ZoomStd now the graph should appear as I described going from neg inf to pos inf passing thru (0,0) as the inflection pts point of inflection is when 2 points change concavity, the tangent line to the graph must exist at the point

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