Letf(x)andg(x) be differentiable functions.

Suppose the linearization off(x)atx=6

is

Lf(x)=7+2(x6)

and the linearization ofg(x)

atx=6

is

Lg(x)=43(x6)

Which of the following statementsmustbe true?Select all that apply.

1)The functionh(x)=144(x6) is a linear approximation to2f(x) atx=6

2)f(6) greater than or equal to g(6)

3)f(6.2) is greater than or equal to g(6.2)

4) The linearization off(x)g(x)atx=6isLfg(x)=2813(x6)

5)The linearization of(f+g)(x)atx=6isLf+g(x)=11(x6)