Question

F(x)=cosx; f(x) + c - ее первообразная, g(x)=f(x) + c - f'(x) и g(0)=2 решите уравнение g(x)=0

Answer 1

$\int{f(x)} \, dx = F(x)+C \\ g(x)=\int{f(x)} \,dx -f'(x) \\ \int{f(x)} \,dx = \int{cos(x)} \,dx=sin(x) \\ f'(x)=(cos(x))'=-sin(x) \\ g(0)=2 \\ sin(0)+C+sin(0)=2 \\ C = 2 \\ g(x)=0 \\ sin(x)+C+sin(x)=0 \\ 2sin(x)+2=0 \\ sin(x)=-1 \\ x = \frac{3\pi}{2}$