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