can you guys figure this tricky one out? ill give a medal!!!

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 how to find the turning point of this function.

Question

can you guys figure this tricky one out? ill give a medal!!!

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 how to find the turning point of this function.

kainui · Answer

So at the turning point, what's the graph look like? What's the slope there and how is it different from everywhere else?

anonymous · Answer

r you asking me bc you don't know or to see if i know?

kainui · Answer

Haha, I know. I'm asking for you to think about what makes this point special or different from all the other points there. I'm helping guide you to understanding.

anonymous · Answer

oh ok lol. i think the special point is where the liquid turns solid?

anonymous · Answer

understanding = win 
the answer = fail

kainui · Answer

Sure, that's the point. But what can you tell me about that point. What is the slope at the turning point? What about the slope at other points before and after that turning point?

anonymous · Answer

whaaa? im completely lost sorry

kainui · Answer

So here's a picture, http://www.wolframalpha.com/input/?i=t%28x%29+%3D+%28x+%2B+5%29+%5E+3+%2B+7 So it looks like this: |dw:1385169063844:dw| Show me where about you think the turning point is.