Find a linearization at a suitably chosen integer near a at which the given function and its derivative are easy to evaluate.
-$$f ( x ) = - 4 x ^ { 2 } - 5 x + 5 , a = 1.1$$
A) L(x) = -4
B) L(x) = 10 - 14x
C) L(x) = -9 - 13x
D) L(x) = 9 - 13x

Question

Quizplus · Accepted Answer

To find a suitable linearization, we need to choose an integer near $a=1.1$. The closest integer is 1. Evaluating $f(x)$ and its derivative at $x=1$, we get $f(1) = -4$ and $f'(1)=-13$. Therefore, the linearization at $x=1$ is $L(x) = f(1) + f'(1)(x-1) = -4 -13(x-1) = 9-13x.$ Therefore, the best choice is D.

Find a Linearization at a Suitably Chosen Integer near a at Which