Question

Calculus????????

Answer 1

$f(x)=(1+x)^6\implies f'(x)=6(1+x)^5\implies f'(0)=6$

At $x=0$, you get $f(0)=(1+0)^6=1$, so the tangent line to $f$ at this point is

$y-1=6(x-0)\implies y=6x+1$

which suggests $f(0.1)\approx6\times0.1+1=1.6$