Question

Identify the maximum and minimum values of the function y = 8 cos x in the interval [-2π, 2π]. Use your understanding of transformations, not your graphing calculator

Answer 1

cool this is rather simple .....
can you tell me the maximum and minimum value of cosx in the interval [-2π, 2π] ?

Answer 2

there are many ways to solve this problem, one way is to sketch the function and spot the max/min, or you may simply use calculus by differentiating the function and setting it to zero

Answer 3

have a look at the plot, and identify the max mountains and min valleys

Answer 4

so how should i put it in for the answer

Answer 5

You know that cosine is bounded:
\[-1\le\cos x\le1\]
What can you say about 8*cosine?
\[?\le8\cos x\le?\]

Answer 6

rite

Answer 7

so put it just like that

Answer 8

Just like what?

Answer 9

can just only put the answer u gave instead of the other part im confused

Answer 10

No, I gave you an interval. You're asked for the maximum and minimum values of 8cosx. If you figure out what the two question marks should be, then you have your answer.

Answer 11

rite

Answer 12

so it woulld be -2pi< 8 cos x <2pi rite

Answer 13

No, that's not it.
\[-1\le\cos x\le1\\
8(-1)\le8(\cos x)\le8(1)\\
-8\le8\cos x\le8\]
This tells you that the highest value attained by 8cosx is 8 and the lowest value is -8.

Answer 14

so it would be min= -8 and max= 8 8 cos x

Answer 15

Yes. The max should be just 8, not "8 8 cosx," though.

Answer 16

so thats all for this problem

Answer 17

Yeah

Answer 18

you should not get confused between the amplitude and frequencies, or y a-xis and x-axis @a2d...

Answer 19

if you look as well to the graph, you can see +8 on the y-axis, and -8

Answer 20

this is another way to visualize max and min

Answer 21

and this is how your AM radio works in communication

Answer 22

rite

Answer 23

go ahead plz

Answer 24

i sent you the graph at the top as well, but the method that Sith gave you is a good one and also important, if you look at the plot you can see on the y axis you have the max is 8 and the min -8

Answer 25

@mathsmind @SithsandGiggles I understand how to get 8 and -8. From there, how do we figure out the x value? (x, 8) and (x, -8)