Question

Am I doing this right? (posting below)

Answer 1

answering below

Answer 2

For the following functions, sketch the graphs of f'(x) and f''(x) on top of the original functions. Remember, a (closed circle) indicates a stationary point, a (open circle) indicates an inflection point, and x indicates a point that is both a stationary point and an inflection point.

Just for number 4...
I'm just confused because I'm not entirely sure what happens when it twists like this

Answer 3

well first off you should give the function you are sketching

Answer 4

I dont know what you mean how are you confused how it twists?

Answer 5

when you get an inflection point it means that the derivative is increasing or decreasing on both sides of the zeros or numbers not in the original function

Answer 6

Here

Answer 7

as you can see from f'(x) inbetween the critical number (I say it is at x =2 because it is on the second notch) you can see that the function stays positive on both sides

Answer 8

this is characteristic of an inflection point

Answer 9

if you understand let me know if not read the stuff I posted. you can also just use wolframalpha to graph your function and its derivatives

Answer 10

when I said, " it means that the derivative is increasing or decreasing on both sides of the zeros or numbers not in the original function" I meant when the derivative is positive on both sides of the critical number or negative on both sides of the critical number

Answer 11

The general rules for graphing functions is provided in the image I posted

Answer 12

It doesn't say what the function is. It just shows the graph and I'm expected to draw the derivatives based on how the function increases and decreases.

Answer 13

I understand everything you said, so did I do it correctly?

Answer 14

yeah seems right to me

Answer 15

just check the rules I posted man if you have those memorized you wont be led astray

Answer 16

Ok thanks for your help

Answer 17

No problem