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

Are you expected to use calculus to solve this question?

Answer 2

nope!

Answer 3

Algebra two....

Answer 4

You can obtain the function \((x+5)^3+7\) by shifting the function \(x^3\) to the LEFT by 5 units and UP by 7 units. If you have seen the \(x^3\) curve you can see where the turning point is. Do you know the turning point of \(x^3\) ?

Answer 5

Strictly speaking, neither the x^3 curve nor the (x+5)^3 + 7 has a turning point as both functions increase in the interval \((-\infty, \infty)\). But there is a point on the curve where the tangent is horizontal and it looks like they are using that as the definition of turning point here and we will go along with it.

Answer 6

Best response @aum