[Calculus] Taylor series

Question

The Taylor series for f(x)=x³ at 1 is ∑∞_N=0 Cn(x-1)ⁿ.

Find the first few coefficients.

C₀=

C₁=

C₂=

C₃=

C₄=

  

I have no clue how to solve this, help greatly appreciated

Answer 1

f(1) = 1³ = 1; f'(x) = 3x²; f'(1) = 3; f''(x) = 6x; f''(1) = 6; f'''(1) = 6; f⁽⁴⁾(x) = 0; f⁽⁴⁾(1) = 0.

C₀ = 1; C₁= 3, C₂ = 6/2! = 3; C₃ = 6/3! = 1; C₄ = 0/4! = 0