Find the linear approximating polynomial for the function centered at a.
-f(x) = tan x, a = $\pi$
A) L(x) = x -2 $\pi$
B) L(x) = x + $\pi$
C) L(x) = x - $\pi$
D) L(x) = 2x - $\pi$

Question

Find the linear approximating polynomial for the function centered at a.
-f(x) = tan x, a =  $\pi$
A) L(x) = x -2  $\pi$
B) L(x) = x +  $\pi$
C) L(x) = x -  $\pi$
D) L(x) = 2x -  $\pi$

Quizplus · Accepted Answer

The linear approximation of a function f(x) at a point a is given by L(x) = f(a) + f'(a)(x - a). For f(x) = tan(x), f(a) = tan(π) = 0 and f'(x) = sec^2(x), so f'(π) = sec^2(π) = 1. Thus, L(x) = 0 + 1(x - π) = x - π.

Find the Linear Approximating Polynomial for the Function Centered at A