Question

f(x) = 3(cos(x))^2 - 6sin(x)
0 ≤ x ≤ 2

Find the intervals on which f is concave down. (Enter the intervals that contain smaller numbers first.) (hint: There are 3 intervals)

Answer 1

what did you get for f''

Answer 2

i got a rock

Answer 3

\[f'(x)=3*2*cosx*(-sinx)-6cosx=-6cosxsinx-6cosx=-6cosx(sinx+1)\]
\[f''(x)=-6*[-sinx*(sinx+1)+cosx(cosx)]=-6[\cos^2x-\sin^2x-sinx]\]
\[f''(x)=-6[1-\sin^2x-\sin^2x-sinx]=-6[-2\sin^2x-sinx+1]\]
set f''=0
so we have
\[-6[-2\sin^2x-sinx+1]=0\]
\[2\sin^2x+sinx-1=0\]
\[2\sin^2x+2sinx-sinx-1=0\]
\[2sinx(sinx+1)-1(sinx+1)=0\]
\[(sinx+1)(2sinx-1)=0\]

Answer 4

my f' got cut off

Answer 5

plus i got 2111 medals, but did anyone congratulate me?
\[\color{blue}{\text{noooooo!}}\]

Answer 6

congrats satellite

Answer 7

yeah my
\[\color{red}{f'}\] got shot off in the war

Answer 8

lol

Answer 9

too little too late. plus i am smokin'! smoking sensei that is . smoking sensei, feeling irie...

Answer 10

so what are the intervals?

Answer 11

are you guys there?

Answer 12

you don't see any of the work i did above?

Answer 13

sinx+1=0 2sinx-1=0
sinx=-1 sinx=1/2
x=3pi/2 x=pi/6, 5pi/6


|------|--------|-----------|----------|
0 pi/6 5pi/6 3pi/2 2pi

plug in a number between each of these numbers to see if is concave up/down
use f''
f'' tells you if the function is concave up or concave down

Answer 14

plug in a number btw 0 and pi/6 into f''

Answer 15

then plug in a number btw pi/6 and 5pi/6 into f''
plug in a number btw 5pi/6 and 3pi/2 into f''
plug in a number btw 3pi/2 and 2pi into f''

Answer 16

i do want to help you k?
i just don't wanna be rushed

Answer 17

f''(.5)=- so concave down on (0,pi/6)
f''(1)=+ so concave up on (pi/6,5pi/6)
f''(3)=- so concave down on (5pi/6, 3pi/2)
f''(5)=- so concave down on (3pi/2, 2pi)

Answer 18

do you got it?

Answer 19

thanks...i ran out of time already!

Answer 20

well that sucks
are you doing an internet course?