Question

A 2-column table with 7 rows. The first column is labeled x with entries negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries 8, 2, 0, negative 2, negative 1, 0, 4.
Which is a possible turning point for the continuous function f(x)?

(–2, 0)
(0, –2)
(2, –1)
(4, 0)

Answer 1

What are your thoughts so far?

Answer 2

I have no clue

Answer 3

Let's look at the first two rows

They tell us we have the points (-6,8) and (-4,2)
What's going on with the y value when we go from y = 8 to y = 2? Is it going up or down?

Answer 4

Down?

Answer 5

yes

Answer 6

now look at the second and third row y values
y = 2
y = 0
Is y going up or down?

Answer 7

down

Answer 8

yes, so the turning point is when y changes direction
so when we go from down to up
more technically: when we go from decreasing to increasing

Example:

that's one example where we go from decreasing to increasing (but we could flip it around to get the same idea)

Answer 9

Thank you

Answer 10

let me know what you get as your answer

Answer 11

(–2, 0)

Answer 12

It might help to plot all the points on the same xy grid

Answer 13

The points go downhill (moving left to right) but then change direction after the turning point

Answer 14

Thanks

Answer 15

No problem

Answer 16

(-2,0) is incorrect but you're fairly close

Answer 17

would it b (0, –2) then?

Answer 18

Check out this graph and the turning point is marked in red

Answer 19

If you drew a curve through those points, it would likely turn at that red point

Answer 20

(0,-2) is correct

Answer 21

Thank you

Answer 22

No problem