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In your lab, a substance\'s temperature has been observed to follow the function

ID: 3168878 • Letter: I

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. 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.

Explanation / Answer

T(x) = (x+5)^3 + 7

to find turning point of the function we take first derivative of this function

T'(x) = 3 ( x+5)^2

setting the derivative equal to 0

3 (x+5)^2 = 0

(x+5)^2 = 0

x = -5

so, turning point occurs at x = -5 because the derivative is 0 at this point