Question

Show that 1+kx is the local linearization of (1+x)^k near x = 0

Answer 1

take the derivative, replace x by 0 to find your slope, then use point - slope formula

Answer 2

\[f(x)=(1+x)^k\]
\[f'(x)=k(1+x)^{k-1}\]
\[f'(0)=k\]
\[y-y_1=m(x=x_1)\]
\[y-1=k(x-0)\]
\[y=1+kx\]