Question

Calc help! Help its 3:17am and I'm crying

Answer 1

Find the x-coordinates where f '(x) = 0 for f(x) = 2x + sin(4x) in the interval [0, π].

Answer 2

f(x) = 2x + sin(4x)

f'(x) = ?

Answer 3

4cos(4x)+2

Answer 4

set that equal to 0

Answer 5

4cos(4x)+2 = 0

is same as

cos(4x) = -1/2

Answer 6

for what angles the cosine function spits out -1/2 ?

Answer 7

do i do arc cos?

Answer 8

you could do that

Answer 9

so 4x=arc cos -1/2?

Answer 10

Yes

Answer 11

x=2.09?

Answer 12

Yes, leave it in exact form as 2pi/3

Answer 13

4x = 2pi/3

Answer 14

But wait, is that the only angle of cosine that gives -1/2 ?

Answer 15

add pi?