Question

se considera functia f:[0,+infinit)->R ,f(x)=√x-1
a)Aratati ca 2√x f'(x)=1
b)sa se calculeze lim x->4 f(x)-f(4)/x-4

Answer 1

a)

f'(x)=(√x-1)'=1/2√x

2√x*f'(x)=2√x*1/2√x=1

b)

Avem formula: lim x->x0 f(x)-f(x0)/x-x0=f'(x). Deci:

lim x->4 f(x)-f(4)/x-4=f'(4)=1/2√4=1/2*2=1/4