reggie98
Answered

Calculus????????


Find the linear approximation that is represented by L(x) for the function:


f(x)= (1+x)^6 at x=0


What does the Error formula give as a rough estimate for the error at x=0.1

Verified Answer :

LammettHash

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

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