Find f if f′′′(x)=sin(x),f(0)=−8,f′(0)=−7,f′′(0)=−7.
f′′′(x)=sin(x)
f"(x) = -cosx + C
since f"(0) = -7,
f"(x) = -cosx - 6
f'(x) = -sinx - 6x + C
since f'(0) = -7,
f'(x) = -sinx - 6x - 7
f(x) = cosx - 3x^2 - 7x + C
since f(0) = -8,
f(x) = cosx - 3x^2 - 7x - 9