1. For a differentiable function f, f' be the funcyion defined by f'(x) lim h->0 =f(x+h)-f(x-h)/(h)

Question

a: Determine f'(x) for f(x)=x
b: Determine f'(x) for f(x)=x^2

Answer 1

I will do the 2nd one, ....

f'(x) = lim ( (x+h)^2 - x^2 )/h , as h --> 0
= lim (x^2 + 2xh + h^2 - x^2)/h
= lim (2xh + h^2)/h , as h -->0
= lim 2x + h , as h --> 0
= 2x

for the 1st one, you should get 1

Answer 2

Thanks ^.^