I feel like I’m doing it right but I keep getting the wrong answer, can someone please work this out so I can see if it’s the website or if it’s me? (the site has glitched before to make right answers wrong).

**Answer 1**

f(x) = 1/x = x^(-1)

f'(x) = – x^(-2)

f”(x) = 2x^(-3)

f”'(x) = – 6 x^(-4)

f(4)=1/4

f'(4)=-1/16

f”(4)= 1/32

f”'(4) = – 1/1536

f(x) = f(4) + f'(4)(x – 4) + f”(4)(x – 4)^2/2 + f”'(4)(x – 4)^3/(3*2)

f(x) = 1/4 – (x – 4)/16 + (x – 4)^2/64 – (x – 4)^3/256

**Answer 2**

the third term would be :

f ‘ ‘ ‘ (4) / 4! * ( x – 4 )^3 / 3 !

f ‘ ‘ ‘ (4) = -3 / 128