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.

Answer 1

find the 1st derivative...

then solve for x, this is a stationary point(s)

find the 2nd derivative....

test the stationary point(s) in the 2nd derivative...

determine the nature, max min or point of inflexion.

substitute the stationary point(s) x, value into the original equation to
get the ordered pair.

hope it helps