Question

Suponha que f(2+h)=3h cos h-1 para todo h. O valor de f ' (2)= ???

Answer 1

Olá, Euler.

 

$<var>f(h)=f[2+(h-2)]=3(h-2)\cos(h-2)-1 \Rightarrow \\\\ f'(h)=3\{(h-2)[-\sin(h-2)] + \cos(h-2)\} \Rightarrow \\\\ f'(2)=3\{0 \cdot [-\sin 0] + \cos 0\}= 3\cdot \{0 +1\}=3 \\\\ \therefore \boxed{f'(2)=3}</var>$