Question

In your lab, a substances 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. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function.

Answer 1

To find the turning points, find the values of x where the derivative is 0.
T(x)=(x-2)^3+8
dy/dx=3(x-2)^2
equating the derivative to 0 we get
3(x-2)^2=0
(x-2)^2=0
x=2

Thus, turning point is at (2,0)