Posted by **Alex** on Thursday, October 3, 2013 at 8:50pm.

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!

- Calculus -
**Steve**, Friday, October 4, 2013 at 12:39am
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

- Calculus -
**Alex**, Friday, October 4, 2013 at 7:38pm
Thanks a lot Steve!

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