Given f''(x)= -4sin(2x) and f'(0)=4 and f(0) =-6. Find f(pi/2)

Answer 1

f" = -4sin2x

f' = 2cos2x + c
2+c = 4
c=2
so, f' = 2cos2x + 2

f = sin2x + 2x + c
0+0+c = -6
c = -6
so, f = sin2x + 2x - 6