# Homework Help: Math approximation problem

1. Oct 28, 2008

### Neil6790

Let f(x) = x^(1/3). The equation of the tangent line to f(x) at x = 8 can be written in the form y = mx+b where m is: and where b is:
Using this, we find our approximation for 8.1^(1.3) is:

I found the slope to be 1/12
I found b to be 1.3333333333333333333
I still can't get the answer for the approximation for 8.1^(1/3).
I plugged it correctly in the mx+b equation but it won't work.

Neil

2. Oct 29, 2008

### Staff: Mentor

Re: Approximation

The exact equation for your tangent line at (8, 2) is
y = 1/12 * x + 4/3

When x = 8.1, what is the value of y on the tangent line? That's your approximation for (8.1)^(1/3).

3. Oct 29, 2008

### HallsofIvy

Re: Approximation

Perhaps simpler: y= (1/12)(x- 8)+ 2.

Edited thanks to Mark44.

Last edited by a moderator: Oct 29, 2008
4. Oct 29, 2008

### Staff: Mentor

Re: Approximation

Halls,
The line has to pass through (8, 2), not (4, 2). You might have overlooked the fact that we're dealing with the cube root function, not the square root function.
Mark

5. Oct 29, 2008

### Neil6790

Re: Approximation

Thanks alot for the help. I was able to get the answer.

Neil