Suppose f”(x) =-36sin(6x) and f’(0)=-5 and f(0)=-6 find f(pi/5)

Answer 1

f" = -36sin(6x)
f' = 6cos(6x)+c
f'(0) = 6+c = -5 --> c = -11
f' = 6cos(6x)-11
f = sin(6x) - 11x + c
f(0) = 0 - 0 + c = -6
f = sin(6x)-11x-6
f(π/5) = sin(6π/5) - 11π/5 - 6 = -13.5