Question

如果f(x)=1/x^1/2,那么[f(a+h)-f(a)]/h=?

Answer 1

f(a+h)-f(a)=

=1/√(a+h)-1/√a

=[√a-√(a+h)]/√(a^2+ah)

=[√a-√(a+h)][√a+√(a+h)]/√(a^2+ah)[√a+√(a+h)]

=(a-a-h)/√(a^2+ah)[√a+√(a+h)]

=-h/√(a^2+ah)[√a+√(a+h)]

所以[f(a+h)-f(a)]/h

=-1/√(a^2+ah)[√a+√(a+h)]