Chapter 4 - Applications of the Derivative - 4.1 Linear Approximation and Applications - Exercises - Page 174: 52

$L(x)$ = $\frac{\pi}{4}(x-1)+\frac{1}{2}$

$f(x)$ = $tan^{-1}x$ $f'(x)$ = $\frac{1}{1+x^{2}}$ $f(a)$ = $f(1)$ = $\frac{\pi}{4}$ $f'(a)$ = $f'(1)$ = $\frac{1}{2}$ $L(x)$ = $f'(a)(x-a)+f(a)$ $L(x)$ = $\frac{\pi}{4}(x-1)+\frac{1}{2}$