Question

Решить уравнение: f(x)=1,5sin2x-5sinx-x, если f``(x)=0

Answer 1

f'(x) = 1,5(sin2x)' - 5(sinx)' - x' = 3cos2x - 5cosx - 1
f''(x) = 3(cos2x)' - 5(cosx)' -1' = -6sin2x + 5sinx = 0
5sinx - 6(2sinxcosx) = 0
5sinx - 12sinxcosx = 0
sinx(5-12cosx)=0
5-12cosx=0
12cosx=5
cosx=5/12=0.416
x = acos(0.416) = 65.4