Linear Approximations estimating given number

Question

F(x)= (x+1)^(1/3)  

X naught = 0

given number is cube root (1.2)

 

 

Please Help! I Don't know how do any of these steps to get this answer. 

Answer 1

f(x) ≈ L(x) = f(x₀) + f'(x₀)(x - x₀)

 

Let f(x) = (x+1)^1/3, x₀ = 0, x = 0.2

 

(1.2)^1/3 = f(0.2) ≈ f(0) + f'(0)(0.2 - 0)

 

                       = (1)^1/3 + (1/3)(1)^-2/3(0.2)

 

                       = 1 + 1/15

 

                       = 16/15