Question

In your lab, a substance's temperature has been observed to follow the function T(x) = (x + 5)3 + 7. The turning point of the graph is where the substance changes from a liquid to a solid. Explain to your fellow scientists how to find the turning point of this function, using complete sentences

Answer 1

Take the derivative of T(x). Setting this to 0 and solving for x, we get x=-5. Since we have a double solution at x=-5 there will be an inflection point. That's where the turning point of the graph is where the substance changes from a liquid to a solid.

Answer 2

This seems an artificial problem.
At the change of phase, the temperature vs time plot will be horizontal awhile due to heat of fusion.