Question

How do you find the maximum and minimum values of the function y = 8 cos x in the interval [-2π, 2π] without using a graphing calculator? I understand getting 8 as max and -8 as min, but how do I figure out the x values? (x, 8) and (x, -8)

Answer 1

What class are you in?

Answer 2

Precalc

Answer 3

take derivative :)

Answer 4

I'm sorry. How would I take the derivative?

Answer 5

\[\left| \cos x \right|\le 1\]
maximum value of cos x=1
maximum value of y=maximum value of 8~cos x=8*1=8
similarly minimum value of cos x=-1
minimum value of y minimum value of 8 cos x=8*-1=-8

Answer 6

@aajugdar I was going to tell her hat but she is only in Pre Calc so there is a different method, you dont learn derivatives and stuff in Pre Calc.

Answer 7

So when asked to write the min and max, I can just write -8 and 8? Don't I need x values?
And yeah, haven't learned derivatives.

Answer 8

oh i see @marissalovescats
i dont have a clue about their education system
my bad
sorry ^^

Answer 9

Haha that's fine, thanks anyways

Answer 10

the other method is to take derivative and put it as 0
it is accurate tho when u hv been given intervals
idk how they came up with this kinda question without teaching derivative ^^

Answer 11

@surjithayer I understand that the y values for the max and min are 8 and -8. How would I get the x values? I need to give the full coordinates for the max and min.

Answer 12

sin x=MP is maximum when x=-3 pi/2,pi/2=OP=1
sin x is minimum when x=-pi/2,3 pi/2=OP'=-1
maximum value of y=8*1=8
minimum value of y=8*-1=-8