Thread: Linear Approximation

Estimate the quantity using Linear Approximation and find the error using a calculator.


The Linear Approximation is:
The error in Linear Approximation is:


I know that:
and the change in x is 4.

So:

f'(x)=-1/2(x)^(-3/2)
f'(a)=-1/2(1/95)^(3/2)
f'(a)=-.000539988606


Change in F=f'(a)*Change in x
So:

delta f=(4)*(-.000539988606)
delta f=-.0021599544


Actual change=f(a+delta x)-f(a)
=f(95+4)-f(95)
=-.0020940537

Error in Approximation= absolute value of (delta f - actual change)
= (-.0021599544-(-.0020940537))
=.000065900717


**Updated with right answers for those that may need help.**

Solved the problem. Updated original post for those that may need help in the future.