Question

Use linear approximation to estimate 15^.25

Answer 1

Or, in other words, use linear estimation to estimate \[\sqrt[4]{15}\]

Answer 2

well \[16^{1/4}=2\]

y(x)=x^1/4

y'(x)= 1/4 x^-3/4

\[y(x+\Delta)=y(x)+y'(x)\Delta x\]

Answer 3

To be honest, I'm kind of confused as to what exactly linear approximation is. I know that the fourth root of 15 is an irrational number; is it essentially a pen and paper method for approximating its value to a relevant number of significant figures?

Answer 4

And thank you for your help so far, by the way.

Answer 5

2+(1/32)(-1)=1.97

Answer 6

Actually it returns pretty accurate number provided that you approximate closed to known value(in our case 16)

Answer 7

Ah, I understand your mathematical logic thus far. So \[\Delta\]x in this case is -1 because you're taking the rate of change at that point in the function and accounting for the change in x-value relative to the y value you originally took (16)?

Answer 8

Yes

Answer 9

Cool, thanks guys.

Answer 10

This may be helpful to you: http://is.gd/8MFOpZ