In your lab, a substance's temperature has been observed to follow the function T(x) = (x - 4)3 + 6. The turning point of the graph is where the substance changes from a liquid to a gas. Explain to your fellow scientists how to find the turning point of this function, using complete sentences.

Question

anonymous · Answer

I just need to know the steps on how to do this. Can someone guide me? 
@skullpatrol @ranga @BTaylor

ranga · Answer

Is this a calculus question?  
If it is a calculus question then you can find the derivative dT/dx, set it to zero and solve for x.

If this is a pre-calculus question, then you can answer is it as follows:

The function T = x^3 has a turning point at x = 0.  We can determine this simply by looking at the graph T = x^3.  Therefore, (0,0) is the turning point for the graph T = x^3.

The function T(x) = (x - 4)^3 + 6 will be the graph T = x^3 shifted to the right by 4 units and shifted up by 6 units.  Therefore, the turning point will also shift from (0,0) to 4 units to the right and 6 units up.  The turning point will be (4,6) for the function T(x) = (x - 4)^3 + 6.

anonymous · Answer

It actually is an Algebra 2 question. Will the above still work? @ranga

ranga · Answer

Yes.

anonymous · Answer

Okay thanks!