Question

Find the absolute minimum value of f(x)= 2sin^2(x) + cos^2(x) on [-pi,pi]

Answer 1

did you find df/dx ?

Answer 2

yeah i think it is 2cos^2(x) - sin^(x) then i set the equation equal to 0 and then i got 2cos^2(x)=sin^2(x) then im not sure what to do after that

Answer 3

Please don't do that. Simplify your life!

2sin^2(x) + cos^2(x) = sin^2(x) + sin^2(x) + cos^2(x) = sin^2(x) + 1

This is why we study trigonometry. The minimum value of sin^2(x) is what?