Question

решите уравнение f'(x)=0,если f(x)=1/2sin^2x-cos2x

Answer 1

f(x) = ½sin²x - cos2x

f'(x) = ½ 2 sinx (sinx)' + sin2x (2x)' = sinxcosx + 4sinxcosx = 5sinxcosx

 

5sinxcosx = 0

sinx = 0

x = πn, n∈Z

cosx = 0

x = π/2 + πn, n∈Z