Curve Sketching

[Dorian Gray]

Greetings everyone,

I need to sketch the following function

y= x^3 + x

However, I seem to be having issues finding the critical values. I always end up with imaginary numbers. I attached a copy of my work.



Any help or guidance is greatly appreciated.

 

[galactus]

That simply means it has no critical values.

 

[Dorian Gray]

Thank you

Thank you both for your input! It is greatly appreciated

@JeffM. Well the derivative would be 3x^2 +1, therefore the graph is always increasing from negative infinity to positive infinity.

 

[Deleted member 4993]

And the slope always >1 (and exists everywhere) → hence slope never = 0 and Critical Point does not exist