# Linear Approximations

1. Dec 6, 2011

### forestmine

1. The problem statement, all variables and given/known data

Find the linear approximation of $\sqrt[3]{27.02}$

2. Relevant equations

f(x)+f'(x)(x-a)

3. The attempt at a solution

So what I did was work with$\sqrt[3]{27}$ since that's an easily known value. So my f(x)=x$^{1/3}$ and my f'(x)=1/3x$^{-2/3}$. From there, I worked f(27) = 3, and f'(27)=1/27.

Then I used the above equation. 3+1/27(x-27). For my value of x, I used 27.02, and got .0004.

Something tells me I'm doing something incorrectly, though...

Thanks for the help!

2. Dec 6, 2011

### hotvette

Are you saying 3+1/27(x-27) = .0004? It has to larger than 3.

3. Dec 6, 2011

### forestmine

My mistake -- calculated that incorrectly. I actually get 3.00074. Was my method correct in that case?

4. Dec 6, 2011

### hotvette

Your method looks ok to me. A good sanity check is to calculate the cube root of 27.02 and compare to the approximation.

Last edited: Dec 6, 2011
5. Dec 6, 2011

### forestmine

Thank goodness for sanity checks. Thanks a lot!