Question

How do you find the linearization at x=8 of `f(x)=lnx`?

Answer 1

`L(x)=f(a)+f'(a)(x-a); f(a)=ln 8, f'(a)=1/8`
`L(x)=ln8+1/8(x-8)=ln8+1/8x -1=1/8x+(ln8-1)`

Explanation:

To find the linearization of f(x) we need to find f(a) and f'(a) then put it into the general equation L(x)=f(a)+f'(a)(x-a) then simplify. Note that a is x which is 8 in this case.