Question

find min and max values of f(x)= cos^2(x)-sin(x) in the interval [0, 2pi]

Answer 1

first, find derrivative of function: F`=-2sin(x)cos(x)-cos(x)=-cos(x)*(sin(x)+1)

Answer 2

ok

Answer 3

then you have to solve equation F`(x)=0: first root is cos(x)=0; x= pi/2 and 3pi/2 and second is sin(x)=-1which is x=3pi/2

Answer 4

hmm...okay so i set f' = 0 and solve to find roots...would those values be where the max and mins occur?

Answer 5

yes, ingeneral they are called extremums, when you find the root, you have to check it in original equation and see, whether it is min or max

Answer 6

okay...so would i use the values to plug in into the original equation to find the max and mins...i think i get it. i would only use the ones that are in the interval, right?

Answer 7

i think i understand it now, thank you for the help!

Answer 8

Plot attached.