Question

The graph of a function is given. Find the approximate coordinates of all points of inflection of the function (if any). (Assume a = 6.) , screen shot of graph included.

Answer 1

since the graph of the function is given this time, the point of inflection occurs where concavity changes...

do you see where on the graph this occurs?

Answer 2

-12,12?

Answer 3

unlike the question i helped you with earlier, this graph is the function itself, not the derivative...
you cannot use what i said earlier with this picture....

Answer 4

ok, so what would the first step in finding the points

Answer 5

do you know the difference between concave up and concave down?

Answer 6

yes.

Answer 7

what interval(s) is the function concave down?
what interval(s) is the function concave up?

Answer 8

-24, 6 for concave down?

Answer 9

not sure for concave up

Answer 10

ok.. let's try it this way...
if you put a tangent line on the graph, going from left to right, the slope would be DECREASING from x=-18 to x=-6, do you see this?

Answer 11

ah yes, ok

Answer 12

and from x=-6 to x=18, the slope of the tangent line will be INCREASING...
so there is a change of concavity at x=-6....

Answer 13

ohh alright

Answer 14

so, do you have the coordinates of the inflection point now?

Answer 15

-18, -6

Answer 16

no...

Answer 17

-18, 6?

Answer 18

no... the change in concavity occurs at x=-6. what is the y value on the function at x=-6 ???

Answer 19

6? sry im confused

Answer 20

yes... so the coordinates of the inflection point of the function is (-6, 6)