In your lab, a substance's temperature has been observed to follow the function T(x) = (x - 2)3 + 8. The turning point of the graph is where the substance changes from a solid to a liquid. Explain to your fellow scientists how to find the turning point of this function, using complete sentences.

please help oh my god im going to friggin lose it over this question.

i'm pretty sure the first step is to find the derivative, but no clue what to do after that.

Question

In your lab, a substance's temperature has been observed to follow the function T(x) = (x - 2)3 + 8. The turning point of the graph is where the substance changes from a solid to a liquid. Explain to your fellow scientists how to find the turning point of this function, using complete sentences.

please help oh my god im going to friggin lose it over this question.

i'm pretty sure the first step is to find the derivative, but no clue what to do after that.

jim_thompson5910 · Answer

The turning point is where the inflection point lies. So you need to take the derivative twice and look for a sign change in T '' (x). 

What do you get for T ' (x) ?

jim_thompson5910 · Answer

Oh sorry, before you look for a sign change, you need to solve T '' (x) = 0

bloosweater · Answer

Uhh, actually I might have made a mistake lol. I need the algebra 2 method, not calculus xD

jim_thompson5910 · Answer

are you in calculus class?

bloosweater · Answer

I read in other questions and kept seeing something about the derivative, but it turns out that's for calculus only. I'm in algebra 2.

jim_thompson5910 · Answer

you mentioned "derivative" so that makes me think you are, but I'm not sure

jim_thompson5910 · Answer

I see

jim_thompson5910 · Answer

ok well for algebra, it's not too bad

the turning point of the parent function y = x^3 is at the origin (0,0)

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jim_thompson5910 · Answer

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