Question

Find the intervals on which f is increasing or decreasing

Answer 1

increasing is when f'(x)>0. decreasing is when f'(x)<0

Answer 2

\[f(x)=sinx+cosx\]

Answer 3

\[0 \le x \le2\pi\]

Answer 4

\[f'(x)=cosx-sinx\]

Answer 5

I am stuck here ;(

Answer 6

Now set that equal to 0:
Cosx - Sinx = 0
Cosx = Sinx

Answer 7

what does that tell me though?

Answer 8

Uhm what are the solutions to that between 0 and 2pi? For what values of x are cos and sin the same?

Answer 9

pi/4

Answer 10

Yea, any others?

Answer 11

no, there shouldnt be?

Answer 12

5pi/4

Answer 13

my bad

Answer 14

:)

Answer 15

f '(x) = 0

cos x - sin x = 0

cos x = sin x

Divide both sides by cos x

1 = (sin x)/(cos x)

1 = tan x

On the interval 0 ≤ x ≤ 2π

x = π/4 or x = 5π/4

Does that help you solve the rest of the problem?

Answer 16

Okay now you got them all :)

Answer 17

so, since pi/4 > 0 thats the increase?

Answer 18

Now you draw this (a little table that i learned from my ap calc teacher a few yrs ago that helps u in function analysis)

Answer 19

pick a value on each of those intervals:
0<=x<=pi/4
pi/4<=x<5pi/4
5pi/4<=x<=2pi