Question

The function f is such that
f(x)= 2sin^2x - 3cos^2x for
0<= x <=pi
State the greatest and least values of f(x)

Answer 1

sin^2x=(1-cos2x)/2
cos^2x=(1+cos2x)/2
=>
f(x)=(-1-5cos(2x))/2
the greatest value is when cos2x is least i.e. at cos2x=-1
f(x)=2
the least value is when cos2x is largest i.e. at cos2x=1
f(x)=-3

Answer 2

find absolute maxima and absolute minima .. in the interval

1) find critical points, y'=0, check for maxima and minima
2) also check for values on boundary
http://www.wolframalpha.com/input/?i=plot+2sin^2x+-+3cos^2x+from+x%3D0+to+x%3Dpi

Answer 3

you know how to find critical points right??

Answer 4

i dont think critical points are necessary for this kindaa problem

Answer 5

@vamgadu can you tell me again, simpler, more explicit, how you solved it?

Answer 6

I need to close this so, just please still help :D thanks

Answer 7

it seems that you are right