Sketch Graph f(x)=x^3 + 1/x | Math Homework Help

[physstudent1]

Homework Statement

Sketch the graph of f(x)=x^3 + 1/x

Homework Equations

The Attempt at a Solution

The only way I could think of doing this was by creating a table of values which I did, my graph came out decently close to the real thing (checked on graphing calculator), we did not learn how to use derivatives to find the increasing and decreasing part so how else would I go about doing this?

 

[rock.freak667]

Well at a stationary point...the first derivative is zero i.e. f'(x)=0.

That will allow you find any stationary point...to find whether it is maximum or minimum points

say you got $$(x_1,f(x_1))$$ as a stationary point then you'd find $$f''(x_1)$$ and if it is +ve then that point is a min. but if it was -ve then it is a max.

also you should check what happens as $$x\rightarrow \pm\infty,0$$

 

[physstudent1]

thanks