How Can You Approximate 8.1^(1/3) Using a Tangent Line?

[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.
Is there another way to do this? Please help.


Neil

 

[Mark44]

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).

 

[HallsofIvy]

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

Edited thanks to Mark44.

 

[Mark44]

Perhaps simpler: y= (1/12)(x- 4)+ 2

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

 

[Neil6790]

Thanks a lot for the help. I was able to get the answer.




Neil