Question

35
CalcDerp102
Find the critical points of the function in the given interval. Then determine if each critical point is is a relative maximum, a relative minimum, or neither. f(x)=4sin2x+2cos4x ; [0,pi]

I have the derivative, im at a stand still

Answer 1

once you have the derivative solve for zero to find your critical points for that interval
then draw a number line with you critical points as values on the number line and test if the derivative is positive or negative on either end and in between the critical points
if the first derivative goes from positive to negative a local max occurs
if the first derivative goes from negative to positive a local minimum occurs
this has to do with the first derivative being the slope of the graph at that exact moment

Answer 2

Do you need more help?

Answer 3

what are the critical points? You get the derivative and u solve for x?

Answer 4

yes you solve for x when the derivative is equal to zero

Answer 5

critical points also exist when the derivative DNE but I do not believe you should encounter this in this instance

Answer 6

is this correct for the derivative :
8cos2x-8sin4x

Answer 7

that is the correct derivative

Answer 8

yes that is correct you should factor out and 8 to get cos(2x)-sin(4x) or cos(2x)=sin(4x)

Answer 9

cos(2x)=sin(2*2x)
cos(2x)=2sin(2x)*cos(2x)
1=2sin(2x)
1/2 = sin(2x)

Answer 10

now could you just divide: sin(4x)/cos(2x) to get your first value?

Answer 11

oh alright.

Answer 12

you need to use the trig identity sin(2x) = 2sin(x)cos(x) but replace the x in the identity with 2x

Answer 13

when you get an equation like that your first reaction should be to look at your trig identities

Answer 14

so the denominator will be 4? and the critical points will be somewhere between [0,pi] which will be part of the numerator...right??

Answer 15

let 2x = u
solve the equation 0.5 = sin(u) for the interval [0,pi]
then solve for x using the values of u you just calculated out
you are confusing me by talking about denominators and numerators the way you are

Answer 16

Sorry my mistake since it is 2x you should increase the interval when solving for u to [0,2pi]

Answer 17

as the locations between pi and 2 pi should be within 0 and pi after solving for x

Answer 18

in this interval only two roots exist when x = pi/12 and when x = 5pi/12

Answer 19

These are your critical values you need to renter values into our original derivative to test if the derivative is positive or negative on each side of every critical number but make sure to choose values within your interval

Answer 20

use my first post to locate the maxs and mins from that point

Answer 21

lol i'll give u lots of medal cause ur doing most of the work THANK YOU!

Answer 22

Also for the absolute max or min do not forget to test the endpoints as well just remember the endpoints are not local maxs or mins they can only be absolute

Answer 23

again derp if your question has been answered then do not forget to close it

Answer 24

thank you! i understand it