Question

Use the linear approximation (1+x)^k\approx 1+kx to find an approximation for the function f(x) for values of x near zero.

I need help for (3+3x)^(1/3). Please help me!

Answer 1

f'(x) = (3x+3)^(-2/3)
f'(0) = 3^(-2/3)
f(0) = 3^(1/3)
So, near x=0,
y-3^(1/3) = 3^(-2/3) x

you can see this graphically at wolframalpha.com if you enter

plot y = (3+3x)^(1/3),y = 3^(-2/3) x + 3^(1/3) for -1<x<1

Answer 2

Thanks a lot Steve!