F.6 Functions

Since the value=0 for third derivative and onwards, it is asily observed that the function is a second degree function, i.e., f(x)=ax²+bx+c
f(-3)=9a-3b+c=1-----(1)
f'(x)=2ax+b=>f'(-3)=-6a+b=-2-------(2)
f''(x)=2a=>a=-1/2
By substituting a=-1/2 in (1) and (2)
b=-5, c=-19/2
∴f(x)=(-1/2)x²-5x-19/2