Question

In your lab, a substance's temperature has been observed to follow the function T()- (x- 2)3 +8. The turning point of the graph is where the substance changes from asolid to a liquid. Using complete sentences in your written answer, explain to yourfellow scientists how to find the turning point of this function. Hint: The turningpoint of the graph is similar to the vertex of a quadratic function. (10 points)

Answer 1

We have the function:

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

A turning point happens when the function reaches a maximum or a minimum.

In that points the value of the first derivative of the function is equal to 0.

So we can find the turning points by finding the first derivative and equal to zero:

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