Question

Fine the point of inflection of the graph

f (x) = 2csc (3x/2) , (0, 2π)

please help me

Answer 1

can someone please help me

Answer 2

Ah. Inflections. How fun. So do you understand what a point of inflection is?

Answer 3

yeah i just despise trig.lol

Answer 4

Haha okay. Well walk through this with me. You want to find the points of inflection, which is when the DERIVATIVE changes from positive to negative or negative to positive.

Answer 5

yeh..

Answer 6

So that means that the second derivative will be what at that point?

Answer 7

ugh im really bad at trig..i can do the simple ones its just the trig ones that are confusing..omg i have 5 mins left...its an online test question omg could u d you just work it out and give it to me..i feel so abd but if you dont mind

Answer 8

Refer to the picture.

Answer 9

Ah no. I'll try to help you work through it, but I don't give answers.

Answer 10

But you need to take the 2nd derivative and then set it equal to 0 to solve for x.

Answer 11

but i dont even knwo how to get the second deritivitve

Answer 12

Take the first derivative first. Then take the second. The derivation rule for csc(x) is -csc(x)cot(x), but you need to use chain rule also.

Answer 13

Derivative of cosecant is -csc*cot

Answer 14

oh wait oki i think i got it...y''=9/4(cos(3x)+3)csc^3(3x/2)

Answer 15

then what do i do after the second derivitve

Answer 16

If that is the correect second derivative, you need to find where it is equal to 0.

Answer 17

Then check values on both sides of it to ensure that the sign changes, then you will know you have an inflection point.

Answer 18

i honestly do not know how to go further on this one when it comes to making it equal zero

Answer 19

cosine(x) is equal to 0 for x a multiple of pi. cosecant is never equal to 0.

Answer 20

http://www.wolframalpha.com/input/?i=plot+cosine%28x%29%2C+cosecant%28x%29

Answer 21

So the expression is equal to 0 when cos(3x)=0

Answer 22

You really need to take it from there though.