f(x_(o)+ Δx) ≈ f(x_(o)) + df(x_(o))
df(x_(o)) =f`(x_(o))* Δx
[b]f(x_(o)+ Δx) ≈ f(x_(o)) + f`(x_(o))* Δx[/b]
f(x)=∛x
f`(x)=(1/3)*(1/∛x^2)
∛65=∛(64+1)=4∛(1+(1/64))
x_(o)=1
Δx=(1/64)
f`(1)=(1/3)*(1/∛1^2)=1/3
∛65=∛(64+1)=4∛(1+(1/64)) ≈ 4*(∛1+(1/3)*(1/64))=4*(1+(1/192))=...