How come on my "thank you notes" that some people sent it from e.g 'someone from San Francisco, America" and then some people have their names attached to it? I hope my question makes sense

Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"