The McLaurin series expansion of that function about x=25 is
f(x) = f(25) + (x-25)[f'(x) at x=25)
f'(x) = (1/2)*x^(-1/2)
f'(25) = (1/2)/5 = 1/10
Therefore
f(x) = 5 + (x-25)/10
f(25.2) = 5+ .02 = 5.02
There is nothing wrong with your answer. The correct value is
5.01996016...
Maybe they wanted you to do the last step and compute an actual numerical approximation, 5.02.
Find the linearization of f(x)= sqrtx at x=25 and use the linearization to approximate sqrt25.2
This is my math: 5+ 1/10 * (25.2-25) but it's wrong.
2 answers
I typed in 5.01999999999 and it took it. Weird.