Answer
x = $-1$ tangent line is y = $\frac{1}{2}x+1$
x = $1$ tangent line is y = $-\frac{1}{2}x+1$
Work Step by Step
f(x) = $\frac{1}{x^{2}+1}$
f'(x) = $\frac{-2x}{(x^{2}+1)^{2}}$
x = $-1$ tangent line is
y = $f'(-1)(x+1)+f(-1)$
y = $\frac{2}{2^{2}}(x+1)+\frac{1}{2}$
y = $\frac{1}{2}x+1$
x = $1$ tangent line is
y = $f'(1)(x-1)+f(1)$
y = $\frac{-2}{2^{2}}(x-1)+\frac{1}{2}$
y = $-\frac{1}{2}x+1$
