Question

sin^2x - cosx on the interval (0,2pi), im asked to find the intervals of increase and decrease...

Answer 1

does f'(x)= 2sinxcosx + sinx?

Answer 2

yes its the f'(x)

Answer 3

when f'(x) positive - increase
f'(x) negative - decrease
f'(x) 0 = stays same

Answer 4

so then i would have 2sinxcosx= -sinx because i have to set it equal to zero, so can i say that 2sinx=-tanx?

Answer 5

solve = 0 and study the sign of the f'(x)

Answer 6

i would divide it by sinx to get 2cosx=-1

Answer 7

right, good thinking, so then cos x= -1/2 and x=2pi/3 and 5pi/3

Answer 8

cosx=-1/2
remembering the trig circle, -1/2 is 2pi/3 and 4pi/3

Answer 9

oops 4pi/3

Answer 10

ya u got it. after u study the sign

Answer 11

and thats it

Answer 12

ok thank you so much