.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.
can any body help ??

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.
can any body help ??

anonymous · Answer

@radar  could you help me im new
to openstudy

campbell_st · Answer

so is it 

$$T(x) = (x - 2)^3 + 8$$

anonymous · Answer

yeah @campbell_st

campbell_st · Answer

well find the 1st derivative $$T'(x) = 3(x - 2)^2 $$ now to find the stationary point set T'(x) to zero and solve for x $$0 = 3(x - 2)^2$$ so the startionary point is x = 2 next find the 2nd derivative $$T"(x) = 6(x - 2)$$ so test the stationary point in T"(x) to determine its nature... T"(2) = 0 so the point x = 2 is a horizontal point of inflection. this is where the cruve changes from concave down to concave up. so the curve has no turning point... to check graph the curve on this site https://www.desmos.com/calculator so perhaps the point of inflection is where it changes states