(b) Now linearization of `f(x)=6x^2-5x+6` near `x_0=3` .
This is the required linearization of f(x) near x_0=3.
Given function is f(x)=`6x^2-5x+6` .
To linearize a function f(x) near a point `x=x_0` , we symply give the Taylor's expansion of the first order about `x=x_0.`
i.e. `L(x_0)=f(x_0)+(x-x_0)f'(x_0)` where `f'=d/dx f(x)`
Now (a) we want to linearize the given function f(x) near `x_0=8` .
so, `f'(8)=12.8-5=91` .
Now Linearization of f(x) near `x_0=8` is given by