Chapter 4 - Applications of the Derivative - 4.1 Linear Approximation and Applications - Exercises - Page 174: 55

8

Linearization of $ f(x)$ at $ x=a $ is $ L(x)=f(a)+f'(a)(x-a)$ Therefore, the linearization at x=2 is $ L(x)=f(2)+f'(2)(x-2)$ $\implies f(2)+f'(2)(x-2)=2x+4$ $\implies f(2)+f'(2)\times x+f'(2)\times-2=2x+4$ $\implies f'(2)=2$ and $ f(2)-2\times f'(2)=4$ which gives $ f(2)=4+(2\times f'(2))=4+(2\times2)=8$