Question

In your lab, a substance's temperature has been observed to follow the function T(x) = (x - 4)3 + 6. The turning point of the graph is where the substance changes from a liquid to a gas. Explain to your fellow scientists how to find the turning point of this function, using complete sentences.

Answer 1

To find the turning point of the function T(x) = (x - 4)^3 + 6, First, find the derivative of T(x), i.e. T'(x) = 3(x - 4)^2 = 3(x^2 - 8x + 16). Next, equate the derivative to zero and solve. The value(s) obtained after solving are the x-values of the turning point. Then plug the x-values into the original equation to obtain the y-values of the turning point.