Question

can someone explain me how to do this STEP BY STEP ?

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. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function.

Answer 1

In order to find the turning point, you need to find the rate of change of the slope.

At the turning point, the slope will be 0.

So, you should take the derivative of T(x): 

T(x)' = 3(x+5)^2, you will see only when x = -5, T(x)' = 0

So when x < -5, T(x)' >0, and x>-5, T(x)' > 0 as well

Therefore, the turning point is unique: x= -5