Question

In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 4)3 + 6. The turning point of the graph is where the substance changes from a liquid to a gas. 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. @dan815

Answer 1

\[T(x) = (x − 4)^3 + 6\]

Answer 2

Yes that's the equation

Answer 3

okay so at a turning point the slope =0

Answer 4

Can you tell me what the derivative of this function is

Answer 5

Uhh i do not know

Answer 6

have you learnt how to take derivatives yet

Answer 7

if u havent then you have to know what y=x^3 graph looks like

Answer 8

No.. What's a derivative

Answer 9

oh okay, then its fine, dont worry about it

Answer 10

What does y=x^3 look like

Answer 11

something like that?

Answer 12

okay yep, so where is the turning point for this graph

Answer 13

X=0

Answer 14

okay so now when we apply transformations

Answer 15

this point will be shifted

Answer 16

right now the turning point is at (0,0)

Answer 17

see each transformation one at a time

Answer 18

y=x^3+6 <---- if we apply only 6, so everywhere you see x^3 we add 6 to all of it