Answer
$L(x)=10x-13$
Work Step by Step
Given: $f(x)=x^3-2x+3$
L(x)=f(a)+f'(a)(x-a)
$f'(x)=3x^2-2$
a=2
$f(2)=2^3-2\times2+3=7$
$f'(2)=3\times2^2-2=10$
then $L(x)=7+10(x-2)$
$L(x)=7+10x-20=10x-13$
$L(x)=10x-13$
Thus, the final answer: $L(x)=10x-13$
